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Floer homology in low-dimensional topology

Organized by: Matthew Hedden, Tom Mrowka, Olga Plamenevskaya, Jacob Rasmussen

April 27-May 1, 2020 

This workshop will explore topics of current interest in the theory of Floer homology for 3-manifolds. Floer homology is a powerful tool for studying the topology of 3- and 4-dimensional manifolds, and the relations between them. The first such invariants were introduced by Floer, and arose in the context of Donaldson theory on smooth 4-manifolds.

In the thirty years since Floer introduced his instanton homology, the theory of Floer homology for 3-manifolds has continuously grown and developed, offering new insights and applications at each turn. There are a wide variety of ways to define the Floer homology of a 3-manifold. Many of these are now known to be equivalent, but their relation to the original instanton homology remains mysterious. Topics which the workshop will emphasize

• Equivariant Floer homology, including Pin(2)-equivariant monopole Floer homology, involutive Heegaard Floer homology, and equivariant Floer theories in symplectic topology;

• The relationship between Floer homology, taut foliations on a 3-manifold, and left orderings of its fundamental group;

• Invariants of 3-manifolds with boundary and corresponding relative invariants of tangles;

• Relations between different Floer theories, with an emphasis on those between instanton Floer homologies and the other flavors of Floer homology (monopole, Heegaard, ECH);

• Concordance and homology cobordism invariants derived from Floer homology.

A unifying goal of the workshop is to better understand the geometric content of Floer homologies. We aim to bring together researchers in Floer homology and related fields (e.g. foliations, concordance and homology cobordism, symplectic geometry) which have a bearing on the subjects above.