String Topology


Alexander A. Voronov

University of Minnesota and Northeastern University

Northeastern University

Thursday, January 22, 2004


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   String Topology was introduced a few years ago by M. Chas and D. Sullivan, who defined a new algebraic structure, that of a BV-algebra, on the homology of the free loop space in a manifold. This structure describes interaction of strings (loops) in the manifold and mimics the Gromov-Witten invariants in a purely topological setting. I will discuss String Topology, as well as a higher-dimensional generalization of it, where strings get replaced by spheres. This generalization is related to Hochschild cohomology and a conjecture of Kontsevich. I will present a computation of the homology of sphere spaces generalizing results of Burghelea and Fiedorowicz on the homology of loop spaces. Some of this is joint work in progress with Sullivan.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Maxim Braverman.

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Posted:: January 17, 2004    URL: