Elements of Algebraic Topology,9780201627282

Elements of Algebraic Topology

by
ISBN13: 9780201627282
ISBN10: 0201627280
Format: Paperback
Pub. Date: 1993-12-01
Publisher(s): CRC Press
List Price: $102.98

Buy New

Usually Ships in 5-7 Business Days
$98.08
Add to Cart

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:180 Days access
Downloadable:180 Days
$125.40
Online:365 Days access
Downloadable:365 Days
$148.20
Online:1825 Days access
Downloadable:Lifetime Access
$228.00
*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
$125.40*
Add to Cart

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $49.69

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Table of Contents

Preface vii
Homology Groups of a Simplicial Complex
1(78)
Simplices
2(5)
Simplicial Complexes and Simplicial Maps
7(8)
Abstract Simplicial Complexes
15(5)
Review of Abelian Groups
20(6)
Homology Groups
26(7)
Homology Groups of Surfaces
33(8)
Zero-dimensional Homology
41(2)
The Homology of a Cone
43(4)
Relative Homology
47(4)
Homology with Arbitrary Coefficients
51(2)
The Computability of Homology Groups
53(9)
Homomorphisms Induced by Simplicial Maps
62(9)
Chain Complexes and Acyclic Carriers
71(8)
Topological Invariance of the Homology Groups
79(50)
Simplicial Approximations
80(3)
Barycentric Subdivision
83(6)
The Simplicial Approximation Theorem
89(6)
The Algebra of Subdivision
95(5)
Topological Invariance of the Homology Groups
100(3)
Homomorphisms Induced by Homotopic Maps
103(8)
Review of Quotient Spaces
111(5)
Application: Maps of Spheres
116(5)
Application: The Lefschetz Fixed-point Theorem
121(8)
Relative Homology and the Eilenberg-Steenrod Axioms
129(32)
The Exact Homology Sequence
129(7)
The Zig-zag Lemma
136(6)
Mayer-Vietoris Sequences
142(3)
The Eilenberg-Steenrod Axioms
145(4)
The Axioms for Simplicial Theory
149(5)
Categories and Functors
154(7)
Singular Homology Theory
161(84)
The Singular Homology Groups
162(6)
The Axioms for Singular Theory
168(7)
Excision in Singular Homology
175(8)
Acyclic Models
183(3)
Mayer-Vietoris Sequences
186(4)
The Isomorphism Between Simplicial and Singular Homology
190(6)
Application: Local Homology Groups and Manifolds
196(6)
Application: The Jordan Curve Theorem
202(7)
More on Quotient Spaces
209(5)
CW Complexes
214(8)
The Homology of CW Complexes
222(9)
Application: Projective Spaces and Lens Spaces
231(14)
Cohomology
245(54)
The Hom Functor
245(6)
Simplicial Cohomology Groups
251(6)
Relative Cohomology
257(5)
Cohomology Theory
262(8)
The Cohomology of Free Chain Complexes
270(9)
Chain Equivalences in Free Chain Complexes
279(2)
The Cohomology of CW Complexes
281(4)
Cup Products
285(7)
Cohomology Rings of Surfaces
292(7)
Homology with Coefficients
299(14)
Tensor Products
299(8)
Homology with Arbitrary Coefficients
307(6)
Homological Algebra
313(54)
The Ext Functor
314(6)
The Universal Coefficient Theorem for Cohomology
320(7)
Torsion Products
327(5)
The Universal Coefficient Theorem for Homology
332(2)
Other Universal Coefficient Theorems
334(4)
Tensor Products of Chain Complexes
338(3)
The Kunneth Theorem
341(9)
The Eilenberg-Zilber Theorem
350(3)
The Kunneth Theorem for Cohomology
353(7)
Application: The Cohomology Ring of a Product Space
360(7)
Duality in Manifolds
367(80)
The Join of Two Complexes
368(6)
Homology Manifolds
374(3)
The Dual Block Complex
377(5)
Poincare Duality
382(6)
Cap Products
388(6)
A Second Proof of Poincare Duality
394(5)
Application: Cohomology Rings of Manifolds
399(9)
Application: Homotopy Classification of Lens Spaces
408(6)
Lefschetz Duality
414(10)
Alexander Duality
424(2)
``Natural'' Versions of Lefschetz and Alexander Duality
426(7)
Cech Cohomology
433(12)
Alexander-Pontryagin Duality
445(2)
Bibliography 447(2)
Index 449

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.