Topological geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1981
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 486 S. graph. Darst. |
| ISBN: | 0521231604 0521298393 |
Internformat
MARC
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| 100 | 1 | |a Porteous, Ian R. |d 1930-2011 |e Verfasser |0 (DE-588)139752633 |4 aut | |
| 245 | 1 | 0 | |a Topological geometry |c Ian R. Porteous |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1981 | |
| 300 | |a 486 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 7 | |a Topologie |2 ram | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Topology | |
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| 650 | 0 | 7 | |a Topologische Geometrie |0 (DE-588)4330788-7 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001488969 | ||
Datensatz im Suchindex
| _version_ | 1804116723573456896 |
|---|---|
| adam_text | CONTENTS
Foreword —2
Acknowledgments; references and symbols
Chapter 0 Guide 1
Chapter 1 Maps 4
Membership; maps; subsets and quotients; forwards and back¬
wards; pairs; equivalences; products on a set; union and inter¬
section; natural numbers; products on w; 2 and II; order
properties of co
Chapter 2 Real and complex numbers 26
Groups; rings; polynomials; ordered rings; absolute value; the
ring of integers; fields; the rational field; bounded subsets;
the notation; the real field; convergence; the complex field;
the exponential maps
Chapter 3 Linear spaces 53
Linear spaces; linear maps; linear sections; linear subspaces;
linear injections and surjections; linear products; linear spaces
of linear maps; bilinear maps; algebras; matrices; the algebras
*K; one sided ideals; modules
Chapter 4 Affine spaces 74
Affine spaces; translations; affine maps; affine subspaces; affine
subspaces of a linear space; lines in an affine space; convexity;
affine products; comment
Chapter 5 Quotient structures 85
Linear quotients; quotient groups; ideals; exact sequences;
diagram chasing; the dual of an exact sequence; more diagram
chasing; sections of a linear surjection; analogues for group
maps; group actions
Chapter 6 Finite dimensional spaces 100
Linear dependence; the basis theorem; rank; matrices; finite
dimensional algebras; minimal left ideals
5
—4 contents
Chapter 7 Determinants 116
Frames; elementary basic framings; permutations of n; the
determinant; transposition; determinants of endomorphisms;
the absolute determinant; applications; the sides of a hyper
plane; orientation
Chapter 8 Direct sum 132
Direct sum; 2K modules and maps; linear complements; com¬
plements and quotients; spaces of linear complements; Grass
mannians
Chapter 9 Orthogonal spaces 146
Real orthogonal spaces; invertible elements; linear correlations;
non degenerate spaces; orthogonal maps; adjoints; examples of
adjoints; orthogonal annihilators; the basis theorem; reflections;
signature; Witt decompositions; neutral spaces; positive definite
spaces; euclidean spaces; spheres; complex orthogonal spaces
Chapter 10 Quaternions 174
The algebra H; automorphisms and anti automorphisms of H;
rotations of R4; linear spaces over H; tensor product of algebras;
automorphisms and anti automorphisms of *K
Chapter 11 Correlations 198
Semi linear maps; correlations; equivalent correlations; algebra
anti involutions; correlated spaces; detailed classification
theorems; positive definite spaces; particular adjoint anti
involutions; groups of correlated automorphisms
Chapter 12 Quadric Grassmannians 223
Grassmannians; quadric Grassmannians; affine quadrics; real
affine quadrics; charts on quadric Grassmannians; Grassman¬
nians as coset spaces; quadric Grassmannians as coset spaces;
Cayley charts; Grassmannians as quadric Grassmannians;
further coset space representations
Chapter 13 Clifford algebras 240
Orthonormal subsets; the dimension of a Clifford algebra;
universal Clifford algebras; construction of the algebras; com¬
plex Clifford algebras; involuted fields; involutions and anti
involutions; the Clifford group; the uses of conjugation; the
map N; the Pfaffian chart; Spin groups; The Radon Hurwitz
numbers
contents —3
Chapter 14 The Cayley algebra 277
Real division algebras; alternative division algebras; the Cayley
algebra; Hamilton triangles; Cayley triangles; further results;
the Cayley projective line and plane
Chapter 15 Normed linear spaces 288
Norms; open and closed balls; open and closed sets; continuity;
complete normed affine spaces; equivalence of norms; the norm
of a continuous linear map; continuous bilinear maps; inversion
Chapter 16 Topological spaces 311
Topologies; continuity; subspaces and quotient spaces; closed
sets; limits; covers; compact spaces; Hausdorff spaces; open,
closed and compact maps; product topology; connectedness
Chapter 17 Topological groups and manifolds 336
Topological groups; homogeneous spaces; topological mani¬
folds; Grassmannians; quadric Grassmannians; invariance of
domain
Chapter 18 Affine approximation 353
Tangency; differentiable maps; complex differentiable maps;
properties of differentials; singularities of a map
Chapter 19 The inverse function theorem 375
The increment formula; the inverse function theorem; the
implicit function theorem; smooth subsets; local maxima and
minima; the rank theorem; the fundamental theorem of algebra;
higher differentials
Chapter 20 Smooth manifolds 399
Smooth manifolds and maps; submanifolds and products of
manifolds; dimension; tangent bundles and maps; particular
tangent spaces; smooth embeddings and projections; embed
dings of projective planes; tangent vector fields; Lie groups;
Lie algebras
Chapter 21 Triality 435
Transitive actions on spheres; the first few diagrams; getting
further; the companion involution; the triality automorphism;
the group G2; the action of Spin 9 on S15; the action of Spin 10
onS31; G2 as a Lie group; other aspects of triality; quadrictriality
Bibliography 463 List of symbols 467 Index 475
|
| any_adam_object | 1 |
| author | Porteous, Ian R. 1930-2011 |
| author_GND | (DE-588)139752633 |
| author_facet | Porteous, Ian R. 1930-2011 |
| author_role | aut |
| author_sort | Porteous, Ian R. 1930-2011 |
| author_variant | i r p ir irp |
| building | Verbundindex |
| bvnumber | BV002265868 |
| callnumber-first | Q - Science |
| callnumber-label | QA564 |
| callnumber-raw | QA564 |
| callnumber-search | QA564 |
| callnumber-sort | QA 3564 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 |
| ctrlnum | (OCoLC)5990411 (DE-599)BVBBV002265868 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002265868 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:03Z |
| institution | BVB |
| isbn | 0521231604 0521298393 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488969 |
| oclc_num | 5990411 |
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| physical | 486 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Porteous, Ian R. 1930-2011 Verfasser (DE-588)139752633 aut Topological geometry Ian R. Porteous 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1981 486 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Géométrie algébrique ram Topologie ram Algebras, Linear Approximation theory Geometry, Algebraic Topology Topologie (DE-588)4060425-1 gnd rswk-swf Topologische Geometrie (DE-588)4330788-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Affine Approximation (DE-588)4141562-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Geometrie (DE-588)4020236-7 s Topologie (DE-588)4060425-1 s DE-604 Affine Approximation (DE-588)4141562-0 s Topologische Geometrie (DE-588)4330788-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Porteous, Ian R. 1930-2011 Topological geometry Géométrie algébrique ram Topologie ram Algebras, Linear Approximation theory Geometry, Algebraic Topology Topologie (DE-588)4060425-1 gnd Topologische Geometrie (DE-588)4330788-7 gnd Geometrie (DE-588)4020236-7 gnd Affine Approximation (DE-588)4141562-0 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4330788-7 (DE-588)4020236-7 (DE-588)4141562-0 (DE-588)4151278-9 |
| title | Topological geometry |
| title_auth | Topological geometry |
| title_exact_search | Topological geometry |
| title_full | Topological geometry Ian R. Porteous |
| title_fullStr | Topological geometry Ian R. Porteous |
| title_full_unstemmed | Topological geometry Ian R. Porteous |
| title_short | Topological geometry |
| title_sort | topological geometry |
| topic | Géométrie algébrique ram Topologie ram Algebras, Linear Approximation theory Geometry, Algebraic Topology Topologie (DE-588)4060425-1 gnd Topologische Geometrie (DE-588)4330788-7 gnd Geometrie (DE-588)4020236-7 gnd Affine Approximation (DE-588)4141562-0 gnd |
| topic_facet | Géométrie algébrique Topologie Algebras, Linear Approximation theory Geometry, Algebraic Topology Topologische Geometrie Geometrie Affine Approximation Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT porteousianr topologicalgeometry |