Algebraic Geometry and Topological Strings Seminar 

02/11/2005, 17:00 — 18:00 — Amphitheatre Pa3, Mathematics Building
Ralph Cohen, Stanford University

String Topology and Holomorphic Curves in the Cotangent Bundle

In this lecture I will give an overview of ``String topology''. This is a purely topological theory first introduced by Chas and Sullivan, that has developed into a vast topological field theory of structure on the homology of loop spaces of manifolds, and in spaces of paths with boundary values in D-branes. I will describe a Morse theoretic viewpoint of string topology. This involves representing moduli space of Riemann surfaces by a category of ribbon graphs. Using this together with analytic work of Salaman and Weber, we relate string topology operations on the loop space LM, with the Gromov Witten theory of the cotangent bundle T*M.

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REFERENCES:

M. Chas and D. Sullivan, String Topology, math.GT/9911159. To appear in Ann. of Math.
R.L. Cohen, Morse theory, graphs, and string topology, math.GT/0411272. To appear in Proc. SMS/NATO Adv. study inst. on Morse theoretic methods in nonlinear analysis and symplectic topology, Kluwer press, 2005.
R.L. Cohen and V. Godin, A polarized view of string topology, Topology, Geometry, and Quantum Field Theory, London Math. Soc. Lecture Notes, vol. 308 (2004) 127-154.
R.L. Cohen and J.D.S. Jones, A homotopy theoretic realization of string topology, Math. Annalen, 324 (2002) 773-798.
R.L. Cohen and A. Voronov, Notes on String Topology, math.GT/0503625. To appear in CRM Lecture Notes from summer school on string topology and Hochschild homology, Almeria Spain, 2005.
D. Sullivan, Open and closed string field theory interpreted in classical algebraic topology, Topology, geometry and quantum field theory, London Math. Soc. Lecture Notes, 308, Cambridge Univ. Press, Cambridge, 2004, math.QA/0302332, p. 344-357.