Course

M660 - Advanced Topology

Course No: 
M660
Credit: 
4
Approval: 
2014
PG-Core
Syllabus: 
  • Homotopy Theory: Fundamental groups and its functorial properties, examples, Van-Kampen Theorem, [8 lectures]
  • Covering spaces: Covering spaces, Computation of fundamental groups using coverings. The classification of covering spaces. Deck transformations. [8 lectures]
  • Simply connected spaces: Simply connected spaces-Universal covering spaces of locally simply connected and pathwise connected spaces. - Universal covering group of connected subgroups of General Linear groups. [16 lectures]
  • Homology groups: Affine spaces, simplexes and chains - Homology groups - Properties of Homology groups. - Chain Complexes, Relation Between one dimensional Homotopy and Homology groups. - (As in sections 8 - 12 of Part II of Greenberg and Harper.) [16 lectures]
Reference Books: 
  1. Armstrong, Basic Topology, Springer, 1983
  2. Greenberg & Harper, Algebraic Topology: A First Course, Addition Wesley, 1984.
  3. Munkres, Topology, Pearson Education, 2005. 1974

Contact us

School of Mathematical Sciences

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

Tel: +91-674-249-4081

Corporate Site - This is a contributing Drupal Theme
Design by WeebPal.