Symplectic geometry seminar

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Winter Semester 1999/00

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Symplectic Geometry Seminar

Title	Complexity of topological spaces and complexity of triangulated categories
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Location	NO E 39 Sonneggstrasse 5, 8092 Zürich
Abstract	There are several different notions of "complexity" for a topological space M. For instance, when M is a manifold one can study: the Lebesgue covering dimension; sum of Betti numbers; minimal number of Morse critical values; or the Lusternik–Schnirelmann category. Similarly, given a triangulated category C, one can measure its complexity using invariants such as the Rouquier dimension; diagonal dimension; or minimal length of presentation as a homotopy colimit. In this talk, I will discuss some of the relations between these categorical invariants and topological invariants when the category C is the Fukaya category of the cotangent bundle of M (equivalently, the category of modules over chains on the based loop space on M). I will mostly focus on - introducing the above invariants of topological spaces and categories and - discussing how Lagrangian cobordisms play a role in bounding the diagonal dimension of C in terms of the minimal number of critical values of a Morse function on M.

Complexity of topological spaces and complexity of triangulated categoriesread_more

NO E 39
Sonneggstrasse 5, 8092 Zürich

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