Featured Speaker

Mladen Bestvin

The principal speaker for the workshop is Professor Mladen Bestvina of the University of Utah. He presented a series of three one-hour lectures.

Video

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1. PL Morse theory

   Introduction to PL Morse theory. Affine polyhedral complexes and the Morse lemma. Application: the Solomon-Tits theorem. Arc complex of a punctured surface.

   • Part 1 - 373 MB - 105 MB
2. Finiteness properties of groups

   Proof, using PL Morse theory, that the arc complex of a disk with punctures on the boundary is a sphere, and otherwise it is contractible. Definition of various finiteness properties of groups. The Eilenberg-Ganea conjecture. The Kervaire-Laudenbach conjecture.

   • Part 2 - 356 MB - 100 MB
3. Applications

   Mapping class groups have type VF. Kernels of right angled Artin groups. Potential counterexamples to Eilenberg-Ganea. A controlled topology conjecture that would imply that Eilenberg-Ganea is false.

   • Part 3 - 329 MB - 95 MB