Syllabus 1. CW-complexes, cellular homology, comparison with singular theory, computation of homology of projective spaces.
2. Definition of singular cohomology, axiomatic properties,
statement of universal coefficient theorem for cohomology. Betti numbers
and Euler characterisitic. Cup and cap product,
Poincare duality. Cross product and statement of Kunneth theorem. Degree
of maps with applications to spheres.
3. Definition of higher
homotopy groups, homotopy exact sequence of a
pair. Definition of fibration, examples of fibrations, homotopy exact
sequence of a fibration, its application to computation of homotopy
groups. Hurewicz homomorphism, The Hurewicz
theorem. The Whitehead Theorem.
Suggested Texts :
1. A. Hatcher, Algebraic Topology, Cambridge University Press (2002).
2. M. J. Greenberg and J.R. Harper,
Algebraic topology: A First Course, Benjamin/ Cummings (1981).
3. E. Spanier, Algebraic Topology, Springer-Verlag (1982).
4. J.W. Vick, Homology Theory: an introduction to
algebraic topology, Springer (1994).
5. J. R. Munkres, Elements of algebraic topology, Addison-Wesley (1984).
6. G.E. Bredon, Topology and Geometry, Springer (Indian reprint
2005)
https://www.isibang.ac.in/~adean/infsys/database/MMath/T3.html
- Teacher: Aniruddha C Naolekar