Department of Mathematics

Geometry and Topology

  •  Siddhi Krishna, Boston College
  •  Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
  •  10/18/2018
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall

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 use branched surfaces to build taut foliations for manifolds obtained by surgery on positive 3-braid closures. As an example, we'll construct taut foliations in every non-L-space obtained by surgery along the P(-2,3,7) pretzel knot. No background in Heegaard-Floer or foliation theories will be assumed.

 

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Michigan State University
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