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His office is room of the Math Building, phone extension , or you can contact him by email. His office hours are Mondays and Fridays , or by appointment. Homework grader: Krishna Kaipa, office in room of the Math Building. Texts: Topology and Geometry by Glen E. Bredon , Graduate Texts in Math.

In this semester, we'll cover the fundamental group, homology, and some basics of manifold topology. Basically, we'll cover Chapters of the required text, which is. A useful list of errata is also available. Prerequisites: The needed background for this course is: The basics of point-set topology: metric spaces, open and closed sets, continuous functions, and ideally general topological spaces. For instance, Math covers all of this and much more. If you are not familiar with general topological spaces, but just the specific example of metric spaces, please read one of the below or similar sources before class starts: Munkres, Topology , Sections 12, 17, and

Office: Altgeld. It develops the theory of cohomology, which is homology's algebraically dual sibling, and applies it to a wide range of geometric problems. A key advantage of cohomology over homology is that it has a multiplication, called the cup product, which makes it into a ring; for manifolds, this product corresponds to the exterior multiplication of differential forms. The other major topic covered in this course are the higher homotopy groups, including things like cellular approximation, Whitehead's theorem, excision, the Hurewicz Theorem, Eilenberg-MacLane spaces, and representability of cohomology. You can download the full text for free here.

Point-set topology: basic definitions, theorems, and examples Covering spaces and the fundamental group: group actions, deck transformations, classification and existence of covering spaces, van Kampen theorem Homology: Hurewicz theorem, Eilenberg—Steenrod axioms, simplicial and singular homology, fixed point theorems. There will be weekly homework assignments, to be done in groups of two, and handed in before the tutorials i. There will be a final oral exam. The homework, midterm and final exam may be completed in either German or English.

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