Related papers: Monopole Floer Homology and Real Structures
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. We…
We establish a structural understanding of the involutive Heegaard Floer homology for all linear combinations of almost-rational (AR) plumbed three-manifolds. We use this to show that the Neumann-Siebenmann invariant is a homology cobordism…
Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for…
Motivated by a conjecture of Donaldson and Segal, we take a first step towards defining a new 3-manifold Floer theory, where the complex is defined by a count of Fueter sections of a hyperk\"ahler bundle over the 3-manifold with fibers…
Seiberg-Witten (Floer) theory, Ozsvath-Szabo's Heegaard Floer theory, Hutchings's embedded contact homology, in different stages of development, define (or are expected to define) packages of invariants for 3- and 4-manifolds (including…
Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a…
We study the behavior of $\mathrm{Pin}(2)$-monopole Floer homology under connected sums. After constructing a (partially defined) $\mathcal{A}_{\infty}$-module structure on the $\mathrm{Pin}(2)$-monopole Floer chain complex of a three…
The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with an emphasis on the local equivalence methods coming from…
We recently defined an invariant of contact manifolds with convex boundary in Kronheimer and Mrowka's sutured monopole Floer homology theory. Here, we prove that there is an isomorphism between sutured monopole Floer homology and sutured…
We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a…
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology…
Given a three-manifold with b_1=1 and a nontorsion spin^c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic pro-spectra. Various functors applied to…
We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Ozsvath and Szabo). We show that for these manifolds, the Pin(2)-equivariant monopole Floer…
We provide an explicit computation over the integers of the bar version $\overline{HM}_*$ of the monopole Floer homology of a three-manifold in terms of a new invariant associated to its triple cup product called extended cup homology. This…
Floer homology is a good example of homological invariants living in the infinite dimension. We suggest a way to construct this kind of invariants using only soft essentially finite-dimensional tools; no hard analysis or PDE is involved.…
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to $\mathbb{Z}_4$-equivariant Seiberg-Witten Floer homology. Further,…
We define four versions of equivariant instanton Floer homology ($I^+, I^-, I^\infty$ and $\widetilde I$) for a class of 3-manifolds and $SO(3)$-bundles over them including all rational homology spheres. These versions are analogous to the…
In this paper, we explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer…
We introduce an invariant for trivalent fatgraph spines of a once bordered surface, which takes values in the first homology of the surface. This invariant is the secondary object coming from two 1-cocycles on the dual fatgraph complex, one…
Motivated by conjectures in Heegaard Floer homology, we introduce an invariant HC(Y) of the cohomology ring of a closed 3-manifold Y whose behavior mimics that of the Heegaard Floer homology HF^\infty(Y,s) for s a torsion spin-c structure.…