University Seminar and Topolgy Seminar

Place: Rome Hall 206,

Date and Time: October 27, 2023, 2:00p-3:00p

Title:  Powell's Conjecture on the Goeritz group of the 3-sphere is stably true

Abstract:  The genus g Goeritz group G_g of the 3-sphere is (roughly) the fundamental group of the configuration space of genus g Heegaard surfaces in S^3.  It can be viewed as a natural 3-dimensional analogue of the braid group in S^2.  In 1980 J. Powell proposed that, for any genus g, G_g is generated by 5 elements.  This has been confirmed for g < 4.  Here we show that, for arbitrary g, Powell's Conjecture is true after a single stabilization.  

In rough detail:  There is a natural function G_g ->G_{g+1} obtained by just adding a trivial summand near a prescribed point in the Heegaard surface.  We show that this natural function carries all of G_g to the subgroup of G_{g+1} generated by Powell's proposed generators.