NCMW - Characteristic Classes and Cobordism

Speakers and Syllabus


 Week I:

Saurav:

1. Basic theory of vector bundles (real as well as complex).
2. Homotopical Aspects and classification.
3. Fibre bundles, reduction and extension of structure groups.

Shastri:
1. CW-complexes, CW-structure of Grassmannians and flag manifolds.
2. Cohomology algebra of real and complex projective spaces, of Grassmannians.
3. Orientation on vector bundles, Thom’s isomorphism theorem (proof may be omitted), Leray-Hirsch Theorem.

Tiken:
1. Steifel-Whitney Classes.
2. Euler Classes.
3. Chern and Pontryagin Classes.

Week II:

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

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:List of Resource Persons:

  1. Arvind Nair (TIFR)
  2. M. S. Raghunathan (CEBS)
  3. Nitin Nitsure (TIFR)
  4. Anant R. Shastri (IITB)
  5. Saurav Bouwmik (IITB)
  6. Yogish Holla (TIFR)
  7. Angkom Tiken Singh (NEHU)
  8. Rekha Santanam (IITB)
  9. Sudarshan Gurjar(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   Shastri L Nitin   DISCUSSION
Tue Saurav   Shastri U Nitin  
Wed Saurav   Shastri N Nitin  
Thu Saurav   Tiken C Nitin  
Fri Saurav   Tiken H Nitin  
Sat Shastri   Tiken   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 Yogish   Raghunathan L Arvind   DISCUSSION
Tue Yogish   Raghunathan U Arvind  
Wed Yogish   Raghunathan N Arvind  
Thu Yogish   Raghunathan C Arvind  
Fri Yogish   Raghunathan H  Arvind  
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