Aarhus University Seal / Aarhus Universitets segl

Seminar by Simone Marzioni

Title: The good pants homology

2013.04.30 | Jane Jamshidi

Date Mon 06 May
Time 15:15 16:00
Location Kol-D (1531-211)


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 $H_1(S)$.