9 papers
Naturality in real Heegaard Floer theory
Gary Guth, Ciprian Manolescu
In a previous paper we defined real Heegaard Floer homology, an invariant of three-manifolds equipped with involutions. Here we prove that real Heegaard Floer homology is natural,…
Satellites and telescopes: a concordance formula for bordered Floer homology
Gary Guth, Sungkyung Kang
Given a knot in , its knot Floer completely determines the bordered Floer homology of its complement by a work of Lipshitz--Ozsváth--Thurston. Furthermore, the determinati…
Real sutured Heegaard Floer homology
Fraser Binns, Gary Guth, Yonghan Xiao
We develop a theory of real sutured manifolds and a real Heegaard Floer theory for these manifolds. We develop a notion of real nice diagrams, and prove that our invariant is combi…
Real Heegaard Floer Homology
Gary Guth, Ciprian Manolescu
We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension ; in particular, this applies to double branched covers over knots. Ou…
Immersed Curves and 4-Manifold Invariants
Jesse Cohen, Gary Guth
For 3-manifolds with torus boundary, the bordered Heegaard Floer invariants of Lipshitz--Ozsváth--Thurston have a geometric interpretation as immersed multi-curves with local syste…
Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence
Gary Guth, Sungkyung Kang
We prove that the Lipshitz-Ozsváth-Thurston correspondence between extended type D structures of knot complements and knot Floer complexes can be arranged s…
Doubled Disks and Satellite Surfaces
Gary Guth, Kyle Hayden, Sungkyung Kang +1
Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks o…
For Exotic Surfaces with Boundary, One Stabilization is Not Enough
Gary Guth
A result of Baykur-Sunukjian states that homologous surfaces in a 4-manifold become isotopic after a finite number of internal stabilizations, i.e. attaching tubes to the surfaces.…
Ribbon Homology Cobordisms and Link Floer Homology
Gary Guth
We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Z…