AIS Algebraic Topology (2016)

Speakers with their affiliations

Topics actually covered:

Time-Table

References:

1. Marvin J. Greenberg and John R. Harper - Algebraic Topology – a first course, Benjamin, 1981
2. Edwin H. Spanier - Algebraic Topology, Tata-Mc Graw Hill
3. Allen Hatcher - Algebraic Topology, 2001
4. Robert M. Switzer - Algebraic Topology- Homotopy and Homology, Sringer-Verlag, 1976.
5. R.E. Mosher and M.C. Tangora – Cohomology operations and applications in homotopy theory, Harper & Row, Publishers, 1968.
6. Adams, J.F. Stable Homotopy and Generalised Homology.
7. Complex cobordism and stable homotopy groups of spheres, D. Ravenel. Academic Press.
8. Milnor - Morse Theory.
9. Gromoll, Meyer - Periodic geodesics on compact Riemannian manifolds.
10. Bott - On the iteration of closed geodesics and Strum intersection theory.
11. 11. Further reading:
12. Gromoll, Meyer - On differentiable functions with isolated critical points.
13. Abraham - Transversality in manifold of mappings.
14. Anant R. Shastri: Basic Algebraic Topology, CRC Press, Taylor and Francis group, 2013.
15. MILNOR J., ``Differential Topology'', Volume 3 of his collected papers, Amer. Math. Soc. 2007. Surgery theory was initiated by Milnor in the period 1956-1960 for the purpose of classifying smooth manifolds that are homotopy equivalent to a sphere of dimension \geq 5. In addition to published research articles, this volume contains four sets of notes for lectures he gave in this period; these lectures had remained in mimeographed form until their formal publication in this volume. They still provide excellent instruction in differential topology.
16. MILNOR J., Morse theory, (based on lecture notes by M. Spivak and R. Wells) Annals of Mathematical Studies No. 51, Princeton University Press, 1963.
17. MILNOR J., Topology from the Differentiable Viewpoint, Univ. Pross of Virginia at Charlotesville, 1965.
18. MILNOR J. and STASHEFF J., Characteristic classes, Annals of Mathematics Studies No. 76, Princeton University Press, 1974. This monograph is based on more succinct mimeographed notes by Milnor and Stasheff for lectures of Milnor given in 1959 and still available at <http://www.maths.ed.ac.uk/~aar/papers/milnorcc.pdf>.
19. Mukherjee, Amiya, Topics in Differential Topology, Hindistan Book Agency, 2005.
20. Shastri, A.R., Elements of Differential Topology, CRC Press, 2011.
21. STEENROD Norman J. , Topology of Fibre bundles, Princeton, 1951; Landmarks in Mathematics and Physics; Princeton, 1999.

There are many more new books and resources in the internet.

 How to reach

1. Come to Guwahati Airport/Railway Station by Air/Train.
2. Accommodation is booked in the New NEHU Guest House, NEHU Campus, Shillong-793022.
3. Enter the campus by Gate no. 2 and at the gate ask the security guards for the direction to the New NEHU Guest House.
4. Take a shared Taxi from Airport to NEHU campus, or take a shared Taxi/ Sumo from the Railway station to NEHU Campus. 
   (Most taxis go to town and NEHU  Campus is out of the way, so you may have to take a local taxi from town to the NEHU Campus, which will charge about Rs. 200/-. Sometimes the taxi from Guwahati agrees to drop you at New Guest House at the NEHU Campus for this they may charge some extra money say Rs. 150 to 200 in addition to usual fare)
5. It may be raining some times, so carry umbrellas/raincoats. On a rainy day temperature drops so carry at least a half sweater.
6. Important local telephone/mobile No.s :
• 0364-2725800 (New NEHU Guest House),
• 09863020684 (Angom Tiken Singh)
• 09863022257 (Sainkupar Mawiong)
• 09402951147 (Ph Chinglensana)