Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- The Fundamental Group: Homotopy and path homotopy, contractible
spaces, deformation retracts, Fundamental groups, Covering spaces,
Lifting lemmas and their applications, Existence of Universal covering
spaces, Galois covering, Seifert-van Kampen theorem and its
application.
- Higher Homotopy Groups: Cobrations, Cober homotopy equivalence,
Fibration, Fiber homotopy equivalence. Co-fiber sequences, Fiber
sequences, Higher homotopy groups, long exact sequences associated to
brations, CW complexes, Homotopy excision and suspension theorems.
- Homology and Cohomology: Simplicial and singular homology: Simplicial
complexes, barycentric subdivision and its uses, Singular homology,
Homotopy invariance, Excision theorems, Mayer-Vietoris sequences,
Homology with arbitrary coecients, Singular cohomology, cup products,
cohomology ring, Poincaré duality.
- J. Peter May, A concise course in Algebraic Topology, Chicago
Lectures in Mathematics, Univ. Chicago Press (1999).
- Allen Hatcher, Algebraic Topology, Cambridge University Press
(2002); online available at the author's webpage:
http BBC//www.math.cornell.edu/ hatcher/AT/ATpage.html
