UID:
almafu_9959239091502883
Format:
1 online resource (363 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88422-0
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1-107-36622-4
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1-107-37095-7
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1-107-36131-1
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1-107-36996-7
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1-299-40402-2
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1-107-36376-4
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0-511-62937-0
Series Statement:
London Mathematical Society lecture note series ; 99
Uniform Title:
Méthodes de géométrie différentielle en topologie algébrique.
Content:
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.
Note:
Translation of: Metodes de geometrie differentielle en topologie algebrique.
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Cover; Title; Copyright; Contents; Introduction; I ALGEBRAIC PRELIMINARIES; 1 BILINEAR MAPS; 2 TENSOR PRODUCT OF TWO VECTOR SPACES; 2.1 Theorem: This construction can always be performed.; 2.2 Remarks:; 2. 3 Proposition; 2.4 Notation; 2.5 Theorem; 2.6 Corollary:; 2.7 Tensor product of Abelian groups; 3 COMMUTATIVITY. ASSOCIATIVITY; 3.1 Theorem:; 3.2 Theorem:; 3.3 Theorem:; 3.4 Remark:; 4 TENSOR PRODUCT OF LINEAR MAPS; 4.1 Theorem:; 4.2 Remark:; 4. 3 Proposi tion:; 5 TENSOR PRODUCT WITH A DIRECT SUM ( 'DISTRIBUTIVITY'); 5.1 Theorem; 5.2 Corollary; 5.3 Corollary; 6 EXACT SEQUENCES
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6.1 Definitions:6.2 Remark:; 6.3 Examples:; 6.4 Definition:; 6.5 Lemma:; 6.6 Corollary:; 6.7 Theorem:; 6.8 Important Remark:; 6.9 Theorem:; 6.10 Corollary.; 6.11 Remark:; 7 TENSOR ALGEBRA; 7.1 Definitions:; 7.2 Theorem:; 7.3 Remark:; 7.4 Theorem:; 7.5 Remark:; 7.6 Theorem:; 8 EXTERIOR POWERS. EXTERIOR ALGEBRA; 8.1 Definition:; 8.2 Proposition:; 8.3 Definitions:; 8.4 Remark:; 8.5 Theorem:; 8.6 Definition:; 8.7 Theorem:; 8.8 Remark:; 8.9 Theorem:; 8.10 Theorem:; 8.11 Theorem:; 8.12 Theorem:; 9 SYMMETRIC POWERS. SYMMETRIC ALGEBRA; 9.1 Definition:; 9.2 Definition:; 9.3 Theorem:; 9.4 Definition:
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9.5 Theorem:9.6 Theorem:; 9.7 Theorem:; 10 DUALITY; 10.1 Theorem:; 10.2 Corollary:; 10.3 Theorem; 11 MODULES; II DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rn; 0 ELEMENTARY RESULTS OF DIFFERENTIAL CALCULUS; 0.1 First Order; 0.2 Second and Higher Orders; 1 DIFFERENTIAL FORMS; 1.1 -Definition:; 1.2 Definition:; 1.3 Remarks:; 1.4 Theorem:; 1.5 Remark:; 1.6 Notation:; 1.7 Example:; 2 EXTERIOR DIFFERENTIAL; 2.1 Theorem:; 2.2 Example:; 2 . 3 Theorem:; 2.4 Example:; 2.5 Theorem:; 3 INVERSE IMAGE OF A DIFFERENTIAL FORM; 3.1 Theorem:; 3.2 Explicit Formula; 4 DB i?HAM COHOMOLOGY; 4.1 Definition:
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4.2 Remark:4.3 Remark:; 4.4 Theorem:; 5 HOMOTOPY; 5.1 Definition:; 5.2 Structure of (UxR; 5.3 Lemma:; 5.4 Definition:; 5.5 Lemma:; 5.6 Definition:; 5.7 Definition:; 5.8 Theorem:; 5.9 Corollary:; 6 COHOMOLOGY OF Rn; 6 .1 Lemma; 6.2 Lemma:; 6.3 Theorem:; 6.4 Remark:; 7 COHCMOLOGY OF R2\{0}; 7.1 Lemma:; 7.2 Theorem:; 7.3 Technical Lemma:; 7.4 Theorem:; 7.5 Corollary:; 7.6 Theorem:; 7.7 Corollary:; 7.8 Recapitulation:; 8 DIFFERENTIAL FORMS WITH COMPACT SUPPORTS; 8.1 Lemma:; 8.2 Definitions:; 8.3 Important Remark:; 8.4 Theorem:; 8.5 Theorem:; 8.6 Theorem:; 8.7 Remarks:
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III DIFFERENTIABLE MANIFOLDS1 TOPOLOGICAL MANIFOLDS; 1.1 Definition:; 1.2 Remarks; 1.3 Theorem:; 1.4 Theorem:; 1.5 Theorem:; 1.6 Definition:; 2 FIRST EXAMPLES; 2.1 Example:; 2.2 Example:; 2.3 Remark:; 2.4 Definitions:; 2.5 Lemma:; 2.6 Lenma:; 2.7 Theorem:; 2.8 Theorem:; 2.9 Theorem:; 2.10 Theorem:; 3 THE IMPLICIT FUNCTION THEOREM; 3.1 Theorem; 3.2 Corollary.; 3.3 Remark:; 4 EXAMPLES RESUMED; 4.1 Example:; 4.2 Definition:; 4.3 Theorem:; 4.4 Corollary:; 4.5 Remark:; 4.6 Theorem:; 4.7 Definition:; 4.8 Theorem:; 4.10 Theorem:; 4.11 Important Remark:; 4.12 Lemma:; 4.13 Corollary:; 4.14 Theorem:
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4.15 Definition:
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English
Additional Edition:
ISBN 0-521-31714-2
Language:
English
URL:
https://doi.org/10.1017/CBO9780511629372
