Algebraic topology, an introduction

Algebraic Topology, an Introduction......Page 1
Titles in Series......Page filename2_0002.djvu
Title......Page filename2_0003.djvu
Copyright......Page filename2_0004.djvu
Dedication......Page filename2_0005.djvu
Preface to New Printing......Page filename2_0006.djvu
Preface......Page filename2_0007.djvu
Note to the Student......Page filename2_0010.djvu
Contents......Page filename2_0013.djvu
1. Two-dimensional Manifolds......Page filename2_0018.djvu
1. Introduction......Page 19
2. Definition and examples of n-manifolds......Page filename2_0019.djvu
3. Orientable vs. nonorientable manifolds......Page filename2_0020.djvu
4. Examples of compact, connected 2-manifolds......Page filename2_0023.djvu
5. Statement of the classification theorem for compact surfaces......Page filename2_0027.djvu
6. Triangulations of compact surfaces......Page filename2_0032.djvu
7. Proof of theorem 5.1......Page filename2_0035.djvu
8. The Euler characteristic of a surface......Page filename2_0046.djvu
9. Manifolds with boundary......Page filename2_0052.djvu
10. The classification of compact, connected 2-manifolds with boundary......Page filename2_0054.djvu
11. The Euler characteristic of a bordered surface......Page filename2_0059.djvu
12. Models of compact bordered surfaces in Euclidean 3-space......Page filename2_0060.djvu
13. Remarks on noncompact surfaces......Page filename2_0064.djvu
2. The Fundamental Group......Page filename2_0072.djvu
1. Introduction......Page 73
2. Basic notation and terminology......Page filename2_0073.djvu
3. Definition of the fundamental group of a space......Page filename2_0075.djvu
4. The effect of a continuous mapping on the fundamental group......Page filename2_0080.djvu
5. The fundamental group of a circle is infinite cyclic......Page filename2_0085.djvu
6. Application: the Brouwer fixed-point theorem in dimension 2......Page filename2_0091.djvu
7. The fundamental group of a product space......Page filename2_0093.djvu
8. Homotopy type and homotopy equivalence of spaces......Page filename2_0095.djvu
3. Free Groups and Free Products of Groups......Page filename2_0102.djvu
2. The weak product of abelian groups......Page 103
3. Free abelian groups......Page filename2_0106.djvu
4. Free products of groups......Page filename2_0114.djvu
5. Free groups......Page filename2_0119.djvu
6. The presentation of groups by generators and relations......Page filename2_0122.djvu
7. Universal mapping problems......Page filename2_0125.djvu
4. Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications......Page filename2_0130.djvu
1. Introduction......Page 131
2. Statement of proof of the theorem of Seifert and Van Kampen......Page filename2_0131.djvu
3. First application of theorem 2.1......Page filename2_0139.djvu
4. Second application of theorem 2.1......Page filename2_0144.djvu
5. Structure of the fundamental group of a compact surface......Page filename2_0146.djvu
6. Application to knot theory......Page filename2_0153.djvu
5. Covering Spaces......Page filename2_0162.djvu
2. Definition and some examples of covering spaces......Page 163
3. Lifting of paths to a covering space......Page filename2_0168.djvu
4. The fundamental group of a covering space......Page filename2_0171.djvu
5. Lifting of arbitrary maps to a covering space......Page filename2_0172.djvu
6. Homomorphisms and automorphisms of covering spaces......Page filename2_0175.djvu
7. The action of the group π(X,x) on the set p-1(x)......Page filename2_0178.djvu
8. Regular covering spaces and quotient spaces......Page filename2_0181.djvu
9. Application: the Borsuk-Ulam theorem for the 2-sphere......Page filename2_0187.djvu
10. The existence theorem for covering spaces......Page filename2_0190.djvu
11. The induced covering space over a subspace......Page filename2_0194.djvu
12. Point set topology of covering spaces......Page filename2_0197.djvu
6. The Fundamental Group and Covering Spaces of a Graph. Applications to Group Theory......Page filename2_0206.djvu
1. Introduction......Page 207
2. Definition and examples......Page filename2_0207.djvu
3. Basic properties of graphs......Page filename2_0209.djvu
4. Trees......Page filename2_0211.djvu
5. The fundamental group of a graph......Page filename2_0214.djvu
6. The Euler characteristic of a finite graph......Page filename2_0217.djvu
7. Covering spaces of a graph......Page filename2_0218.djvu
8. Generators for a subgroup of free group......Page filename2_0221.djvu
7. The Fundamental Group of Higher-Dimensional Spaces......Page filename2_0228.djvu
1. Introduction......Page 229
2. Adjunction of 2-cells to a space......Page filename2_0229.djvu
3. Adjunction of higher-dimensional cells to a space......Page filename2_0231.djvu
4.  CW-complexes......Page filename2_0232.djvu
5. The Kurosh subgroup theorem......Page filename2_0235.djvu
6. Grushko\'s theorem......Page filename2_0242.djvu
8. Epilogue......Page filename2_0253.djvu
Appendix A. The Quotient Space or Identification Space Topology......Page filename2_0260.djvu
1. Definitions and basic properties......Page 261
2. A generalization of the quotient space topology......Page filename2_0263.djvu
3. Quotient spaces and product spaces......Page filename2_0266.djvu
4. Subspace of a quotient space vs. quotient space of a subspace......Page filename2_0267.djvu
5. Conditions for a quotient space to be a Hausdorff space......Page filename2_0268.djvu
Appendix B. Permutation Groups or Transformation Groups......Page filename2_0271.djvu
1. Basic definitions......Page 272
2. Homogeneous G-spaces......Page filename2_0273.djvu
Index......Page filename2_0276.djvu
Graduate Texts in Mathematics......Page filename2_0279.djvu
Back Cover......Page Massey W. Algebraic topology.. An introduction (Springer, 1977)(ISBN 0387902716)(600dpi)-287.djvu