8 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,…
Undecidability problems for semifree DG algebras
Ciprian Manolescu, Nick Rozenblyum
We prove that the stable tame isomorphism, quasi-isomorphism, and derived Morita equivalence problems for semifree noncommutative differential graded algebras (DGAs) are all undeci…
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…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
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…