Course

M404 - Algebraic Topology

Course No:
M404
Credit:
4
Prerequisites:
M302, M304
Approval:
2014
UG-Core
PG-Elective
Syllabus:
Homotopy Theory: Simply Connected Spaces, Covering Spaces, Universal Covering Spaces, Deck Transformations, Path lifting lemma, Homotopy lifting lemma, Group Actions, Properly discontinuous action, free groups, free product with amalgamation, Seifert-Van Kampen Theorem, Borsuk Ulam Theorem for sphere, Jordan Separation Theorem. Homology Theory:Simplexes, Simplicial Complexes, Triangulation of spaces, Simplicial Chain Complexes, Simplicial Homology, Singular Chain Complexes, Cycles and Boundary, Singular Homology, Relative Homology, Short Exact Sequences, Long Exact Sequences, Mayer-Vietoris sequence, Excision Theorem, Invariance of Domain.
Text Books:
1.  J. R. Munkres, “Topology”, Prentice-Hall of India, 2013.
2. A. Hatcher, “Algebraic Topology”, Cambridge University Press, 2009.
Reference Books:
1. G. E. Bredon, “Topology and Geometry”, Graduates Texts in Mathematics 139, Springer, 2009.