Lectures on algebraic topology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Zürich
European Math. Soc.
2006
|
| Schriftenreihe: | EMS series of lectures in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | 99 S. graph. Darst. |
| ISBN: | 9783037190234 303719023X |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV021758468 | ||
| 003 | DE-604 | ||
| 005 | 20170817 | ||
| 007 | t | ||
| 008 | 061009s2006 d||| |||| 00||| eng d | ||
| 020 | |a 9783037190234 |c Print |9 978-3-03719-023-4 | ||
| 020 | |a 303719023X |c Print |9 3-03719-023-X | ||
| 035 | |a (OCoLC)70619273 | ||
| 035 | |a (DE-599)BVBBV021758468 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 1 | |a eng |h rus | |
| 049 | |a DE-824 |a DE-19 |a DE-703 |a DE-355 |a DE-91G |a DE-11 |a DE-188 |a DE-83 |a DE-29T | ||
| 050 | 0 | |a QA612 | |
| 082 | 0 | |a 514.2 |2 22 | |
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 084 | |a 55-01 |2 msc | ||
| 084 | |a MAT 550f |2 stub | ||
| 100 | 1 | |a Matveev, Sergej V. |d 1947- |e Verfasser |0 (DE-588)124843956 |4 aut | |
| 240 | 1 | 0 | |a Lekcii po algebraičeskoj topologii |
| 245 | 1 | 0 | |a Lectures on algebraic topology |c Sergey V. Matveev |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2006 | |
| 300 | |a 99 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS series of lectures in mathematics | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Algebraic topology | |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Topologie |0 (DE-588)4120861-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n ebook |a Matveev, Sergej V. |t Lectures on algebraic topology |z 978-3-03719-523-9 |w (DE-604)BV036706015 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014971597 | ||
Datensatz im Suchindex
| _version_ | 1804135619562045440 |
|---|---|
| adam_text | Contents
Preface
.
v
1 Elements
of homology theory
]
1.1
Categories and functors
......................... 1
1.2
Some geometric properties of R^
................... 4
1.3
Chain complexes
............................ 7
1.4
Homology groups of a simplicial complex
............... 10
1.5
Simplicial maps
............................. 13
1.6
Induced homomorphisms of homology groups
............. 17
1.7
Degrees of maps between manifolds
.................. 18
1.8
Applications of the degree of a map
.................. 23
1.9
Relative homology
........................... 32
1.10
The exact homology sequence
..................... 33
1.11
Axiomatic point of view on homology
................. 37
1.12
Digression to the theory of Abelian groups
............... 39
1.13
Calculation of homology groups
.................... 41
1.14
Cellular homology
........................... 43
1.15
Lefschetz fixed point theorem
..................... 47
1.16
Homology with coefficients
....................... 50
1.17
Elements of cohomology theory
.................... 53
1.18
The
Poincaré
duality
.......................... 58
2
Elements of homotopy theory
61
2.1
Definition of the fundamental group
.................. 61
2.2
Independence of the choice of the base point
.............. 63
2.3
Presentations of groups
......................... 65
2.4
Calculation of fundamental groups
................... 68
2.5
Wirtinger s presentation
......................... 72
2.6
The higher homotopy groups
...................... 74
2.7
Bundles and exact sequences
...................... 76
2.8
Coverings
................................ 79
Answers, hints, solutions
........................... 83
Bibliography
................................. 95
Index
..................................... 97
|
| adam_txt |
Contents
Preface
.
v
1 Elements
of homology theory
]
1.1
Categories and functors
. 1
1.2
Some geometric properties of R^
. 4
1.3
Chain complexes
. 7
1.4
Homology groups of a simplicial complex
. 10
1.5
Simplicial maps
. 13
1.6
Induced homomorphisms of homology groups
. 17
1.7
Degrees of maps between manifolds
. 18
1.8
Applications of the degree of a map
. 23
1.9
Relative homology
. 32
1.10
The exact homology sequence
. 33
1.11
Axiomatic point of view on homology
. 37
1.12
Digression to the theory of Abelian groups
. 39
1.13
Calculation of homology groups
. 41
1.14
Cellular homology
. 43
1.15
Lefschetz fixed point theorem
. 47
1.16
Homology with coefficients
. 50
1.17
Elements of cohomology theory
. 53
1.18
The
Poincaré
duality
. 58
2
Elements of homotopy theory
61
2.1
Definition of the fundamental group
. 61
2.2
Independence of the choice of the base point
. 63
2.3
Presentations of groups
. 65
2.4
Calculation of fundamental groups
. 68
2.5
Wirtinger's presentation
. 72
2.6
The higher homotopy groups
. 74
2.7
Bundles and exact sequences
. 76
2.8
Coverings
. 79
Answers, hints, solutions
. 83
Bibliography
. 95
Index
. 97 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Matveev, Sergej V. 1947- |
| author_GND | (DE-588)124843956 |
| author_facet | Matveev, Sergej V. 1947- |
| author_role | aut |
| author_sort | Matveev, Sergej V. 1947- |
| author_variant | s v m sv svm |
| building | Verbundindex |
| bvnumber | BV021758468 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
| callnumber-search | QA612 |
| callnumber-sort | QA 3612 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| classification_tum | MAT 550f |
| ctrlnum | (OCoLC)70619273 (DE-599)BVBBV021758468 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01736nam a2200433 c 4500</leader><controlfield tag="001">BV021758468</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170817 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">061009s2006 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783037190234</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-03719-023-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">303719023X</subfield><subfield code="c">Print</subfield><subfield code="9">3-03719-023-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)70619273</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021758468</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514.2</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">55-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 550f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Matveev, Sergej V.</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124843956</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Lekcii po algebraičeskoj topologii</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on algebraic topology</subfield><subfield code="c">Sergey V. Matveev</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Zürich</subfield><subfield code="b">European Math. Soc.</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">99 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">EMS series of lectures in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus d. Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic topology</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Topologie</subfield><subfield code="0">(DE-588)4120861-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Topologie</subfield><subfield code="0">(DE-588)4120861-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">ebook</subfield><subfield code="a">Matveev, Sergej V.</subfield><subfield code="t">Lectures on algebraic topology</subfield><subfield code="z">978-3-03719-523-9</subfield><subfield code="w">(DE-604)BV036706015</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014971597</subfield></datafield></record></collection> |
| id | DE-604.BV021758468 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:34:20Z |
| indexdate | 2024-07-09T20:43:23Z |
| institution | BVB |
| isbn | 9783037190234 303719023X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014971597 |
| oclc_num | 70619273 |
| open_access_boolean | |
| owner | DE-824 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-83 DE-29T |
| owner_facet | DE-824 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-83 DE-29T |
| physical | 99 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | European Math. Soc. |
| record_format | marc |
| series2 | EMS series of lectures in mathematics |
| spelling | Matveev, Sergej V. 1947- Verfasser (DE-588)124843956 aut Lekcii po algebraičeskoj topologii Lectures on algebraic topology Sergey V. Matveev Zürich European Math. Soc. 2006 99 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS series of lectures in mathematics Aus d. Russ. übers. Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 Erscheint auch als ebook Matveev, Sergej V. Lectures on algebraic topology 978-3-03719-523-9 (DE-604)BV036706015 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matveev, Sergej V. 1947- Lectures on algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Lectures on algebraic topology |
| title_alt | Lekcii po algebraičeskoj topologii |
| title_auth | Lectures on algebraic topology |
| title_exact_search | Lectures on algebraic topology |
| title_exact_search_txtP | Lectures on algebraic topology |
| title_full | Lectures on algebraic topology Sergey V. Matveev |
| title_fullStr | Lectures on algebraic topology Sergey V. Matveev |
| title_full_unstemmed | Lectures on algebraic topology Sergey V. Matveev |
| title_short | Lectures on algebraic topology |
| title_sort | lectures on algebraic topology |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT matveevsergejv lekciipoalgebraiceskojtopologii AT matveevsergejv lecturesonalgebraictopology |