Part II

Covering Spaces, CW Complexes and Homology

[369/100%]

Chapter 4Covering spaces[71/100%]

Section 4.1Basic examples and properties[21/100%]

Section 4.2Conjugate subgroups of

\pi_1

and equivalent covering spaces[20/100%]

Section 4.3Covering transformations[18/100%]

Section 4.4The universal covering space and quotient covering spaces[12/100%]

Chapter 5CW complexes[59/100%]

Section 5.1Examples of CW complexes[16/100%]

Section 5.2The fundamental group of a CW complex[16/100%]

Section 5.3Homotopy type and CW complexes[14/100%]

Section 5.4The Seifert--van Kampen theorem for CW complexes[9/100%]

Section 5.5Simplicial complexes and

\Delta

-complexes[4/100%]

Chapter 6Homology[239/100%]

Section 6.1Chain complexes and homology[5/100%]

Section 6.2Homology of a

\Delta

-complex[7/100%]

Section 6.3Singular homology

H_i(X)

and the isomorphism

\pi_1^{ab}(X, x) \simeq H_1(X)

[15/100%]

Section 6.4Cellular homology of a two-dimensional CW complex[8/100%]

Section 6.5Chain maps and homology[12/100%]

Section 6.6Axioms for singular homology[11/100%]

Section 6.7Reformulation of excision and the Mayer--Vietoris exact sequence[9/100%]

Section 6.8Applications of singular homology[21/100%]

Section 6.9The degree of a map

f : S^n \to S^n

[15/100%]

Section 6.10Cellular homology of a CW complex[15/100%]

Section 6.11Cellular homology, singular homology, and Euler characteristic[13/100%]

Section 6.12Applications of the Mayer--Vietoris sequence[22/100%]

Section 6.13Reduced homology[7/100%]

Section 6.14The Jordan curve theorem and its generalizations[16/100%]

Section 6.15Orientation and homology[35/100%]

Section 6.16Proof of homotopy invariance of homology[12/100%]

Section 6.17Proof of the excision property[16/100%]