Simone Marzioni

(University of Bologna )

(University of Bologna )

Seminar

Monday, 6 May, 2013, at 15:15-16:15, in Koll. D (1531-211)

Abstract:

We give an introduction to the Good Pants Homology theory as developed by J. Kahn and V. Markovic. They used such theory, together with their proof of the Surface Subgroup Theorem, to prove the Ehrenpreis Conjecture. An $(\epsilon,R)$-good curve on a closed surface $S$ is a closed geodesic $\gamma$ with length in the interval $[2R-\epsilon,2R+\epsilon]$. An $(\epsilon,R)$-good pair of pants is an immersed three punctured sphere with three $(\epsilon,R)$-good curves as boundary. The Good Pants Homology is the homology theory where cycles are generated by $(\epsilon,R)$-good curves, and boundaries are generated by the boundary of $(\epsilon,R)$-good pair of pants. The main result is that such homology is the same as the singular homology $H_1(S)$.

Organised by: QGM

Contact person: Jørgen Ellegaard Andersen