Introductory lectures on manifold topology: signposts
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Somerville, Mass. [u.a.]
Internat. Press [u.a.]
2014
|
| Schriftenreihe: | Surveys of modern mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. [125] - 126 |
| Beschreibung: | II, 128 S. Ill., graph. Darst. |
| ISBN: | 9781571462879 |
Internformat
MARC
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| 003 | DE-604 | ||
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| 020 | |a 9781571462879 |9 978-1-57146-287-9 | ||
| 035 | |a (OCoLC)897008549 | ||
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| 100 | 1 | |a Farrell, Thomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory lectures on manifold topology |b signposts |c Thomas Farrell ; Yang Su |
| 264 | 1 | |a Somerville, Mass. [u.a.] |b Internat. Press [u.a.] |c 2014 | |
| 300 | |a II, 128 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Surveys of modern mathematics |v 7 | |
| 500 | |a Literaturverz. S. [125] - 126 | ||
| 650 | 0 | 7 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologische Mannigfaltigkeit |0 (DE-588)4185712-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Su, Yang |e Verfasser |0 (DE-588)132855844 |4 aut | |
| 830 | 0 | |a Surveys of modern mathematics |v 7 |w (DE-604)BV041123344 |9 7 | |
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Datensatz im Suchindex
| _version_ | 1804152632622710784 |
|---|---|
| adam_text | Contents
1
Introduction
................................................... 1
2
The /i-Cobordism Theorem
.................................... 5
2.1
The /i-Cobordism Theorem and Generalized
Poincaré
Conjecture
. . 5
2.2
Tangent
vertors,
einbeddings,
isotopie*
......................... 9
2..4
Handles
aiul
haiidlehody decomposition
........................ 1.4
2.-t
Calculus of handle moves
.....................................
is
2.*> Proof of
t
lie /i-Cobordisin Theorem
............................ 29
3
The s-Cobordism Theorem
.................................... 35
3.1
Statement of the s-Cobordism Theorem
........................ 35
.4.2
Whitehead group
............................................ 40
Л. Л
Whitehead torsion for chain complexes
......................... 43
4
Some Classical Results
......................................... 53
4.1
Novikovs Theorem
.......................................... 53
4.2
A counterexample to the Hurewicz Conjecture
.................. 55
4.3
Milnor^s exotic spheres
....................................... 58
4.4
Rochlin s Theorem
........................................... 61
4.5
Proof of Novikov s Theorem
.................................. 64
4.6
Novikov Conjecture
.......................................... 72
5
Exotic Spheres and Surgery
................................... 75
5.1
Plumbing
................................................... 75
5.2
Surgery
.................................................... 80
6 Hauptvermutung.............................................. 89
6.1
The Fundamental Theorem of algebraic A -theory
................ 89
6.2
Edwards-Cannon s example
................................... 98
6.3
The
Haupt
vermut ung........................................
102
6.4
Whitehead torsion
...........................................103
6.5
Proof of Stallings Theorem
...................................108
6.6
Farreli-Hsiang s example
.....................................112
ii
Contents
6.7
The structure set
............................................115
6.8
Siebenmann s example
.......................................120
References
.........................................................125
Index
..............................................................127
Surveys of Modern Mathematics (SMM)
Mathematics has developed to a very high level and continues to progress rapidly. An essential charac¬
teristic of modem^udy and research is a strong interaction between the various areas of mathematici¬
an interaction fruitful and beautifui in its
resulte.
It is crucial to educate new generations of mathemati¬
cians about important existing theory together with new developments in mathematics» and in the proc¬
ess to give s&idents a basis for grasping this
rntefconnectivity
of mathematics.
The book series Surveys of
Modern
Mathematics (5MM) has been created especially to
heíp
provide
such an education
Ш
students
worîdwkte* m
volumes that are both accessible and affordable. Volumes
in the SMM series will consist of lecture notes selected from introductory courses, col lections of impor¬
tant survey papers, and expository monographs on well-known or developing topics.
With joint publication by Higher Education Press of Beijing within China and by International Press of
Boston in the West and elsewhere, the Surveys of Modern Mathematics book series extends a broad
reach to students and general readers worldwide.
Introductory Lectures on Manifold Topology: Signposts
Since the
1950s,
many new ideas and tools from algebra, and algebraic and
geometrìe
topology, have
been applied to study the structure of hfgh-dimensional differential and
topologica!
manifolds, and so
today it can be difficult for beginners to delve through the literature. This volume is a helpful guide to
the basic concepts and results of topology of manifolds—including the h~ and s-cobordlsm theorems,
topologica!
invariance
of
raţionat
Pontryagîn
classes, surgery theory, and
algebrai
с
КЉеосу.
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:48Z |
| institution | BVB |
| isbn | 9781571462879 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027585004 |
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| physical | II, 128 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Internat. Press [u.a.] |
| record_format | marc |
| series | Surveys of modern mathematics |
| series2 | Surveys of modern mathematics |
| spelling | Farrell, Thomas Verfasser aut Introductory lectures on manifold topology signposts Thomas Farrell ; Yang Su Somerville, Mass. [u.a.] Internat. Press [u.a.] 2014 II, 128 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Surveys of modern mathematics 7 Literaturverz. S. [125] - 126 Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Su, Yang Verfasser (DE-588)132855844 aut Surveys of modern mathematics 7 (DE-604)BV041123344 7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027585004&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027585004&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Farrell, Thomas Su, Yang Introductory lectures on manifold topology signposts Surveys of modern mathematics Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| subject_GND | (DE-588)4185712-4 |
| title | Introductory lectures on manifold topology signposts |
| title_auth | Introductory lectures on manifold topology signposts |
| title_exact_search | Introductory lectures on manifold topology signposts |
| title_full | Introductory lectures on manifold topology signposts Thomas Farrell ; Yang Su |
| title_fullStr | Introductory lectures on manifold topology signposts Thomas Farrell ; Yang Su |
| title_full_unstemmed | Introductory lectures on manifold topology signposts Thomas Farrell ; Yang Su |
| title_short | Introductory lectures on manifold topology |
| title_sort | introductory lectures on manifold topology signposts |
| title_sub | signposts |
| topic | Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd |
| topic_facet | Topologische Mannigfaltigkeit |
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