Course

M404 - Algebraic Topology

Course No: 
M404
Credit: 
4
Prerequisites: 
M302
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.

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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