Topology / Topologie

BMS basic course at TU Berlin, Winter 2006/7

0230 L 127 / 128
Mondays 10-12 and 14-16 in room MA 313
Wednesdays 12-14 in room MA 313
Course information is online at
John M. Sullivan, MA 318, tel 314-29279
Office Hours:
Tuesday 11:30-12:30, or by appointment
Frank Aurzada
Analysis, group theory
Course work:
weekly homework assignments,
two written tests,
take-home final exam
Primary Textbooks:
Fulton, Algebraic Topology, GTM 153, Springer
Bredon, Topology and Geometry, GTM 139, Springer
Additional Textbooks:
Hatcher, Algebraic Topology, Cambridge U Press
Jänich, Topologie, Springer
tom Dieck, Topologie, de Gruyter
Lück Algebraische Topologie, Vieweg
This course covers three areas of algebraic topology:

DeRham cohomology in the plane
Path integrals, winding numbers, deRham cohomology, Mayer-Vietoris, fixed point theorems, Jordan curve theorem. (cf. Fulton, Chap. 1-6,10)
Covering spaces and the fundamental group
Fundamental group, Hurewicz theorem, covering spaces, group actions, deck transformations, classification and existence of covering spaces, van Kampen Theorem. (cf. Fulton, Chap. 11-17)
Singular homology
Eilenberg-Steenrod axioms, homology and fundamental group of spheres and tori, fixed point and separation theorems in higher dimensions. (cf. Bredon, Chap. 4)
Each of these topics makes up about a third of the course. The two tests will approximately cover the first two topics, respectively, and will be held in November and January. The take-home final exam covers the whole course.