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Taut Foliations, Positive 3-Braids, and the L-Space Conjecture

Banff International Research Station for Mathematical Innovation and Discovery

The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll build taut foliations for manifolds obtained by surgery on positive 3-braid closures. Our theorem provides the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. As an example, we'll construct taut foliations in every non-L-space obtained by surgery along the P(-2,3,7) pretzel knot.

Mathematics; Algebraic topology; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Boston College

2019-12-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72800

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/