IST Topology (2016)- Speakers and Syllabus

Lecture-wise Breakup (tentative)

  • Lecture 1: Overview.Recalling metric spaces, and definitions via sequences.
  • Lecture 2 and 3: Topological spaces, open and closed sets, subspaces, continuous functions, homeomorphisms, basis of a topological space and product spaces.
  • Lecture 4 and 5: Hausdorff separation axiom, compactness and connectedness.
  • Lecture 6 and 7: Group actions on topological spaces, quotient topology. Examples : Circle, Mobius Strip.
  • Lecture 8 and 9: Homotopy, examples of Homotopy. Homotopy as an equivalence relation.
  • Lecture 10 and 11: Topological manifolds, surfaces. Examples of sphere,torus, Mobius strip, Klein bottle, projective plane etc. Connected sum of surfaces.
  • Lecture 12 and 13: Groups basics. Group structure on loops. Contractible spaces. Path lifting lemma without proof for the circle.
  • Lecture 14 and 15: Simplicial Complexes, triangulation.
  • Lecture 16 and 17: Fundamental group of a circle and covering map.Definition of Covering spaces
  • Lecture 18 and 19: Polygons, polygon presentation. Examples of surfaces.Cutting and pasting.
  • Lecture 20 and 21: Brouwer’s fixed point theorem., Complex numbers, S1 as subspace of C and the Fundamental theorem of Algebra.
  • Lectures 22-23: Classification theorem for surfaces, only showing that every quotient space obtained from a polygonal region in the plane is homeomorphic to either sphere, n torus or m fold projective plane.
  • Lectures 24: Borsuk Ulam theorem.

References

  • Armstrong, M.A. : Basic topology
  • Massey, W.S. : A basic course in algebraic topology
  • Munkres, J. : Topology
  • C Thomassen : The Jordan Schoenflies Theorem and the classification of surfaces.

 

Speakerwise Breakup

Speaker Affiliation Lectures Legend
S. Sane I.I.T. Bombay 1, 4, 5, 24. SS
Sudharshan Gurjar I.I.T. Bombay 2, 3, 6, 7 SDG
Shameek Paul C.B.S Mumbai 8, 9, 12, 13. SP
Ajay Thakur I.S.I. Bangalore 10, 11, 14, 15. AT
Shripad Garge I.I.T. Bombay 16, 17, 20, 21 SPG
Nandini Nilakantan I.I.T. Kanpur 18, 19, 22, 23 NN

 

Timetable

Day 9:30 - 11:00 11:00 - 11:30 11:30-1:00 1:00 - 2:30 2:30 - 3:30 3:30 - 4:00 4:00 - 5:00 5:00
May 9 Lecture 1 - SS Tea Lecture 2 - SDG Lunch Tutorial 1 Tea Tutorial 2 Snacks
May 10 Lecture 3 - SDG Tea Lecture 4 - SS Lunch Tutorial 3 Tea Tutorial 4 Snacks
May 11 Lecture 5 - SS Tea Lecture 6 - SDG Lunch Tutorial 5 Tea Tutorial 6 Snacks
May 12 Lecture 7 - SDG Tea Lecture 8 - SP Lunch Tutorial 7 Tea Tutorial 8 Snacks
May 13 Lecture 9 - SP Tea Lecture 10 - AT Lunch Tutorial 9 Tea Tutorial 10 Snacks
May 14 Lecture 11 - AT Tea Lecture 12 - SP Lunch Tutorial 11 Tea Tutorial 12 Snacks
May 15 SUNDAY
May 16 Lecture 13 - SP Tea Lecture 14 - AT Lunch Tutorial 13 Tea Tutorial 14 Snacks
May 17 Lecture 15 - AT Tea Lecture 16 -SPG Lunch Tutorial 15 Tea Tutorial 16 Snacks
May 18 Lecture 17 -SPG Tea Lecture 18 - NN Lunch Tutorial 17 Tea Tutorial 18 Snacks
May 19 Lecture 19 - NN Tea Lecture 20 -SPG Lunch Tutorial 19 Tea Tutorial 20 Snacks
May 20 Lecture 21 -SPG Tea Lecture 22 - NN Lunch Tutorial 21 Tea Tutorial 22 Snacks
May 21 Lecture 23 - NN Tea Lecture 24 - SS Lunch Tutorial 23 Tea Tutorial 24 Snacks