18 citations · 18 across the 4 of their papers we have counts for
8 papers · 1 filter
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,…
From knots to four-manifolds
Ciprian Manolescu
This is a survey article about the connections between knot theory and four-dimensional topology. Every four-manifold can be represented in terms of a link, by a Kirby diagram. Thi…
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…
Canonical orientations in Heegaard Floer theory
Mohammed Abouzaid, Ciprian Manolescu
We set up Heegaard Floer theory over the integers, using canonical orientations coming from coupled Spin structures on the Lagrangian tori. We prove naturality of Heegaard Floer ho…
A knot Floer stable homotopy type
Ciprian Manolescu, Sucharit Sarkar
Given a grid diagram for a knot or link K in , we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type o…
Searching for ribbons with machine learning
Sergei Gukov, James Halverson, Ciprian Manolescu +1
We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to di…