NCMW - Characteristic Classes and Cobordism

Speakers and Syllabus


 

Week I:

  1. Review of homology and cohomology (as in Appendix A of Milnor’s book).
  2. Cohomology algebra of real and complex projective spaces.
  3. Orientation on vector bundles, Thom’s isomorphism theorem (proof may be omitted), Leray-Hirsch Theorem.
  4. Mod 2 cohomology of infinite Grassmannian.
  5. Basic theory of vector bundles (real as well as complex).
  6. Homotopical Aspects and classification.
  7. Fibre bundles, reduction and extension of structure groups.
  8. Steifel-Whitney Classes.
  9. Euler Classes.
  10. Chern and Pontryagin Classes.

Week II:

  1. Hirzebruch Riemann Roch
  2. Chern-Weil Theory.
  3. Thom’s Cobordism Theorem (unoriented and oriented).

References

  1. Milnor and Stasheff - Characteristic Clases
  2. Allen Hatcher - Vector Bundles and K-Theory
  3. Shigeyuki Morita - Geometry of Characteristic Classes
  4. Dale Husemoller - Fibre Bundles
  5. Hirzebruch - Topological Methods in Algebraic Geometry.
  6. Anant Shastri - Basic Algebraic Topology.

List of Resource Persons:

  1. Prof. M. S. Raghunathan (CEBS)
  2. Nitin Nitsure (TIFR)
  3. Arvind Nair (TIFR)
  4. Anant R. Shastri (IITB)
  5. Saurav Bhaumik (IITB)
  6. Yogish Holla (TIFR)
  7. Angkom Tiken Singh (NEHU)
  8. Sudarshan Gurjar (IITB)
  9. Rekha Santanam (IITB)

Time Table

Week I: 4th to 9th March 2019

  9-30– 11-00 Tea 11-30– 13-00   15-00–00 16-30 Tea/ Snacks 17-00– 18-00
Mon Saurav   Tiken L Yogish   DISCUSSION
Tue Saurav   Tiken U Yogish  
Wed Saurav   Tiken N Yogish  
Thu Saurav   Shastri C Yogish  
Fri Saurav   Shastri H Yogish  
Sat Shastri   Raghunathan   Nitin  

Week II: 11th to 15th March 2019

  9-30– 11-00 Tea 11-30– 13-00   15-00–00 16-30 Tea/ Snacks 17-00– 18-00
Mon Nitin   Raghunathan L Arvind   DISCUSSION
Tue Nitin   Raghunathan U Arvind  
Wed Nitin   Raghunathan N Arvind  
Thu Nitin   Raghunathan C Arvind  
Fri Raghunathan   Arvind H    
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