Topology / Topologie

BMS basic course at TU Berlin, Winter 2010

3236 L 127 / 128
Mondays 10-12 and 12-14 in room MA 313
Wednesdays 14-16 in room MA 644
Course information is online at
John M. Sullivan, MA 318, tel 314-29279
Office Hours:
Tuesdays 11:30-12:30, or by appointment
Silvia De Toffoli, MA 319, tel 314-29280
Office Hours:
Tuesdays 14:30-16:30
Analysis, linear algebra
Course work:
weekly homework assignments,
two written tests,
oral 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 / online
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 scheduled in November and January. The oral final exam covers the whole course.