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math.GT2026
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,…
math.GT2026
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…
math.GT2026
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…