ATMW Topology of Manifolds and Group Actions (2017)- Speakers and Syllabus

Objectives of the Workshop:
The proposed workshop is intended for the benefit of Young Researchers/Lecturers of Mathematics from various Universities and Colleges in India. The workshop will be devoted to a thorough discussion of topological methods currently being used in computing the Cohomological structure of orbit spaces and fixed point sets of compact Lie group actions on manifolds and other topological spaces on the lines of  P. A. Smith theory.  Experts in the area will be requested to present selected topics from topology of Manifolds, Cech Cohomology, fiber bundles, Spectral sequences like the Leray-Serre spectral sequences associated with fiber bundles of Borel’s constructions. Proper emphasis will be given on relevant tutorials which will supplement and enhance the material covered in lectures along with problem solving.

List of Confirmed Speakers:
I. Prof Satya Deo,  HRI, Allahabad
II. Prof Himadri Mukherji, NEHU, Shillog
III. Prof S S Khare, NEHU, Shillong
IV. Prof Tej Bahadur Singh, University of Delhi, Delhi
V. Dr Satya Prakash Tripathi, University of Delhi, Delhi
VI. Dr Hemant Kumar Singh, University of Delhi, Delhi

Topics to be covered:

Speakers

No. of Lectures

Topics

S S Khare (SSK)

5 (1½ Hours)

Topology of Manifolds: Manifolds and Smooth maps, Derivatives and Tangents, Immersions and Submersions

Tej Bahadur Singh

(TBS)

4 (1½ Hours)

Cech Cohomology & Spectral Sequences: The Leray-Serre spectral sequence, Leray-Cartan spectral sequence.

Satya Deo

(SD)

6 (1½ Hours)

Equivariant Cohomologies and Group Actions: Finitistic spaces and their orbit spaces, Milnor Construction, Localization theorem, Generalizations of Smith theory of fixed point sets.

Himadri Mukherji

(HM)

5 (1½ Hours)

Actions on Manifolds: Proper actions, Quotients of Manifolds by group Actions, Covering Manifolds, Homogenous Spaces. Applications.

Satya Prakash Tripathi

(SPT)

2 (1½ Hours)

Topology of Manifolds: Transversality, Orientation, Lefschetz fixed point theory.

Hemant Kumar Singh

(HKS)

2 (1½ Hours)

Topology of Manifolds: Vector fields and Poincare Hopf theorem.

Special Lectures:
I. Prof  P Sankaran. IMSc, Chennai
II. Prof Goutam Mukherji, ISI, Kolkata

  List of confirmed Course Associates:
I. H. K. Singh, University of Delhi, Delhi
II. S. P. Tripathi, Kirori Mal College, University of Delhi, Delhi
III. J. K. Maitra, Rani Durgavati Vishwavidyalaya, Jabalpur, M. P.
IV. Dr Virender Vikram Awasthi, NIT, Nagpur, Maharashtra
V. K. Somorjit, University of Delhi

Recommended Texts:
I. V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, 1974
II. John M. Lee, Introduction to Smooth Manifolds, Springer, 2002
III. J. McCleary, A User’s Guide to Spectral Sequence, Cambridge University Press, 2001
IV. Glen Bredon, Introduction to compact Transformation Groups, Academic Press, 1972.
V. D. Husemöller , Fibre Bundles, Springer-Verlag, Third Edition, 1993

Tentative Time-Table:

 

 

Lecture-1

Tea

Lecture-2

Lunch

Tutorial or Guest Lecture

Tea & Snacks

Day

Date

9.30-11.00

 

11.30 -1.00

1-2.30

2.30-3.30

3.30-4.30

 

Thursday

09/11/17

SSK-1

 

TBS-1

 

 

 

 

Friday

10/11/17

SSK-2

 

TBS-2

 

 

 

 

Saturday

11/11/17

SSK-3

 

TBS-3

 

 

 

 

Sunday

12/11/17

BREAK- SUNDAY

Monday

13/11/17

SSK-4

 

TBS-4

 

 

 

 

Tuesday

14/11/17

SSK-5

 

SD-1

 

Special Lecture-PS

 

 

Wednesday

15/11/17

SPT-1

 

SD-2

 

 

 

 

Thursday

16/11/17

SPT-2

 

SD-3

 

 

 

 

Friday

17/11/17

HKS-1

 

SD-4

 

 

 

 

Saturday

18/11/17

HKS-2

 

SD-5

 

 

 

 

Sunday

19/11/17

BREAK- SUNDAY

Monday

20/11/17

HM-1

 

SD-6

 

Special Lecture-GM

 

 

Tuesday

21/11/17

HM-2

 

HM-3

 

 

 

 

Wednesday

22/11/17

HM-4

 

HM-5