In this course we will treat 2 important methods/techniques in topology and geometry:
(1) singular homology,
(2) sheaves and cohomology.
Both are aimed at understanding the global properties of a topological space by analyzing how the space is built up out of simple pieces. Part (1) will end with a discussion of the Brouwer fixpoint theorem in arbitrary dimension, and the hairy ball theorem.
This course will be an excellent preparation for the courses Riemann surfaces’ andAlgebraic geometry’ from the mastermath program, given in Spring 2010.
Hours
2 hours lecture
Examination
home work exercises and oral exam
Literature
syllabi and notes
Prerequisites
introductory courses on groups, rings, fields and topology. That is, the material covered by the local courses Algebra 1-3 and Topologie.
Links