Course on Algebraic Topology (second semester 2011/2012)

This is a course jointly organized by Moritz Groth and Ieke Moerdijk.
Time and place: Tuesday (first session: January 31), 10.30-12.30, room: HG 03.054

Questions about the exercises (and also the lecture) can be discussed with Matija Bašić and Giovanni Caviglia (room: HG 03.064) each Wednesday from 11.00 to 12.00. Grades will be given based on a presentation at the end of the lecture and an oral examination.

Lecture notes (updated course notes and exercise sheets can be found here):
  Lecture 01   Definition of singular homology, first examples
  Lecture 02   Low-dimensional identifications
  Lecture 03   Some homological algebra, relative singular homology
  Lecture 04   Chain homotopies, singular homology of contractible spaces
  Lecture 05   Homotopy invariance of singular homology
  Lecture 06   Excision property and Mayer-Vietoris sequence
  Lecture 07   Proof of excision property of singular homology
  Lecture 08   Jordan-Brouwer separation theorem
  Lecture 09   Degree of a map, CW-complexes
  Lecture 10   CW-complexes and cellular homology
  Lecture 11   no regular lecture, presentation of projects to students
  Lecture 12   Isomorphism between cellular and singular homology

Projects to be presented by students:
  Project 1:   Simplicial sets and the geometric realization
  Project 2:   Homology with coefficients and universal coefficient theorem
  Project 3:   Galois theory of covering spaces

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