Groups of area preserving homeomorphisms and subleading asymptotics of link spectral invariants

Date: 2022-06-29

Time: 11:00 - 12:00

Zoom link:


Vincent Humiliere


Whether the group G of area preserving homeomorphisms of the 2-sphere is simple remained an open question for a long time, but was finally answered in the negative a couple of years ago by Dan Cristofaro-Gardiner, Sobhan Seyfaddini and myself. The proof shows in particular that the normal subgroup of “hameomorphisms” (denoted Hameo) introduced in the 2000s by Yong-Geun Oh and Stefan Müller is proper. To pursue the study of the group G, a central open question was then whether Hameo was the smallest normal subgroup in G. I will report on very recent joint work with Dan Cristofaro-Gardiner, Cheuk-Yu Mak, Sobhan Seyfaddini and Ivan Smith, which in particular answers this question in the negative as well.

This is based on a study of the subleading asymptotics of the “link spectral invariants” (which we developed in our previous work) that might be of independent interest, and raises new questions about these invariants.