Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Homotopy, retract, deformation retract, contractible spaces and
homotopy type, fundamental group and its properties, The fundamental
group of circle, van Kampen theorem (statement without proof),
applications of van Kampen theorem.
- Simplicial complexes, polyhedra and triangulations, barycentric
subdivision and simplicial approximation theorem.
- Orientation of simplicial complexes, simplicial chain complex and
homology, properties of integral homology groups, induced
homomorphisms. degree of a map from n-sphere to itself and its
applications
- Invariance of simplicial homology groups. Lefschetz fixed point
theorem, Borsuk-Ulam theorem.
- Definition and examples of covering spaces. path lifting and homotopy
lifting property.
- Covering homomorphisms, deck transformations, classification of
Coverings, existence of universal covering (statement without proof).
- Graphs, coverings of graphs and their fundamental groups.
- Satya Deo, Algebraic Topology: A Primer, Texts and Readings in
Mathematics Vol. 27, Hindustan Book Agency (2003).
- William Massey, Algebraic Topology: An Introduction, Springer
(Graduate Texts in Mathematice Vol. 127), (1977).
- Allen Hatcher, Algebraic Topology, Cambridge University Press
(2002).
- M. Greenberg and J. Harper, Algebraic Topology: A First Course,
Addision-Wesley (1981).
- H. Seifert and W. Threlfall, A Textbook of Topology, Academic
Press (1980).
