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Combinatorial and Gauge theoretical methods in low dimensional topology and geometry

Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false?

speaker: Antonio Alfieri (CRM-ISM)

abstract: In a recent note Francesco Lin showed that if a rational homology sphere Y admits a taut foliation then the Heegaard Floer module HF-(Y) contains a copy of FUU as a summand. This implies that either the L-space conjecture is false or that Heegaard Floer homology satisfies a geography restriction. In a recent paper in collaboration with Fraser Binns we verified that Lin's geography restriction holds for a wide class of rational homology spheres. I shall discuss our argument, and advance the hypothesis that the Heegaard Floer module HF-(Y) may satisfy a stronger geography restriction than the one suggested by Lin’s theorem.

timetable:
Tue 4 Jun, 14:00 - 15:00, Aula Dini
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