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Elements of Algebraic Topology by James Munkres
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About this book :-
Elements of Algebraic Topology written by
James Munkres
This book is intended as a text for a first-year graduate course in algebraic topology; it presents the basic material of homology and cohomology theory.
For students who will go on in topology, differential geometry, Lie groups, or homological algebra, the subject is a prerequisite for later work. For other students, it should be part of their general background, along with algebra and real and complex analysis.
Geometric motivation and applications are stressed throughout. The abstract aspects of the subject are introduced gradually, after the groundwork has been laid with specific examples.
The book begins with a treatment of the simplicial homology groups, the most concrete of the homology theories. After a proof of their topological invariance and verification of the Eilenberg-Steenrod axioms, the singular homology groups are introduced as their natural generalization. CW complexes appear as a useful computational tool. This basic "core" material is rounded out with a treatment of cohomology groups and the cohomology ring.
Book Detail :-
Title: Introduction to Topology: Pure and Applied
Edition:
Author(s): James Raymond Munkres
Publisher: Perseus Books
Series:
Year: 1984
Pages: 465
Type: PDF
Language: English
ISBN: 978-0-2016-2728-2,978-0-2010-4586-4,9780429962462,0429962460
Country: US
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About Author :-
Author James Raymond Munkres (born 1930) is a Professor Emeritus of mathematics at MIT and the author of several texts in the area of topology. Munkres completed his undergraduate education at Nebraska Wesleyan University and received his Ph.D. from the University of Michigan in 1956. He was also elected to the 2018 class of fellows of the American Mathematical Society.
Munkres taught at the University of Michigan and at Princeton University before coming to MIT. His area of research work was Topology, Analysis on Manifolds, Elements of Algebraic Topology, and Elementary Differential Topology. He is also the author of Elementary Linear Algebra.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals notes avaliable of this author, We recomended you to download all.
• Elements of Algebraic Topology by James Munkres
• Topología 2.a Edición by James Munkres
• Topology (2E) by James R. Munkres
• Topology A First Course by James Munkres
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Book Contents :-
Elements of Algebraic Topology written by
James Munkres
cover the following topics.
1. Homology Groups of a Simplicial Complex
1 Simplices
2 Simplicial Complexes and Simplicial Maps
3 Abstract Simplicial Complexes
4 Review of Abelian Groups
5 Homology Groups
6 Homology Groups of Surfaces
7 Zero-dimensional Homology
8 The Homology of a Cone
9 Relative Homology
*10 Homology with Arbitrary Coefficients
*11 The Computability of Homology Groups
12 Homomorphisms Induced by Simplicial Maps
13 Chain Complexes and Acyclic Carriers
2. Topological Invariance of the Homology Groups
14 Simplicial Approximations
15 Barycentric Subdivision
16 The Simplicial Approximation Theorem
17 The Algebra of Subdivision
18 Topological Invariance of the Homology Groups
19 Homomorphisms Induced by Homotopic Maps
20 Review of Quotient Spaces
*21 Application: Maps of Spheres
*22 Application: The Lefschetz Fixed-point Theorem
3. Relative Homology and the Eilenberg-Steenrod Axioms
23 The Exact Homology Sequence
24 The Zig-zag Lemma
25 Mayer-Vietoris Sequences
26 The Eilenberg-Steenrod Axioms
27 The Axioms for Simplicial Theory
*28 Categories and Functors
4. Singular Homology Theory
29 The Singular Homology Groups
30 The Axioms for Singular Theory
31 Excision in Singular Homology
*32 Acyclic Models
33 Mayer-Vietoris Sequences
34 The Isomorphism Between Simplicial and Singular Homology
*535 Application: Local Homology Groups and Manifolds
*36 Application: The Jordan Curve Theorem
37 More on Quotient Spaces
38 CW Complexes
39 The Homology of CW Complexes
*40 Application: Projective Spaces and Lens Spaces
5. Cohomology
41 The Horn Functor
42 Simplicial Cohomology Groups
43 Relative Cohomology
44 Cohomology Theory
45 The Cohomology of Free Chain Complexes
*46 Chain Equivalences in Free Chain Complexes
47 The Cohomology of CW Complexes
48 Cup Products 285
49 Cohomology Rings of Surfaces
6. Homology with Coefficients
50 Tensor Products
51 Homology with Arbitrary Coefficients
7. Homological Algebra
52 The Ext Functor
53 The Universal Coefficient Theorem for Cohomology
54 Torsion Products
55 The Universal Coefficient Theorem for Homology
*56 Other Universal Coefficient Theorems
57 Tensor Products of Chain Complexes
58 The Kiinneth Theorem
59 The Eilenberg-Zilber Theorem
*60 The Kiinneth Theorem for Cohomology
*61 Application: The Cohomology Ring of a Product Space
8. Duality in Manifolds
62 The Join of Two Complexes
63 Homology Manifolds
64 The Dual Block Complex
65 Poincare Duality
66 Cap Products
67 A Second Proof of Poincare Duality
*68 Application: Cohomology Rings of Manifolds
*69 Application: Homotopy Classification of Lens Spaces
70 Lefschetz Duality
71 Alexander Duality
72 "Natural" Versions of Lefschetz and Alexander Duality
73 Cech Cohomology
74 Alexander-Pontryagin Duality
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