Related papers: Contact structures, excisions, and sutured monopol…
Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanced sutured manifolds. In this paper, we introduce…
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured monopole Floer homology theory (SHM). Our invariant can be viewed as a generalization of Kronheimer and Mrowka's contact invariant for…
We use monopole Floer homology to study the topology of the space of contact structures on a 3-manifold. Our main tool is a generalisation of the Kronheimer--Mrowka--Ozsv\'ath--Szab\'o contact invariant to an invariant for families of…
We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it…
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…
This article is a standalone introduction to sutured Floer homology for graduate students in geometry and topology. It is divided into three parts. The first part is an introductory level exposition of Lagrangian Floer homology. The second…
The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for…
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…
These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation with the four-dimensional theory, our…
In this paper, we generalize the work of the second author and prove a grading shifting property, in sutured monopole and instanton Floer theories, for general balanced sutured manifolds. This result has a few consequences. First, we offer…
Using contact-geometric techniques and sutured Floer homology, we present an alternate formulation of the minus and plus version of knot Floer homology. We further show how natural constructions in the realm of contact geometry give rise to…
We prove the equivalence of the sutured versions of Heegaard Floer homology, monopole Floer homology, and embedded contact homology. As applications we show that the knot versions of Heegaard Floer homology and embedded contact homology are…
We use monopole Floer homology for sutured manifolds to construct invariants of Legendrian knots in a contact 3-manifold. These invariants assign to a knot K in Y elements of the monopole knot homology KHM(-Y,K), and they strongly resemble…
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured instanton Floer homology theory. To the best of our knowledge, this is the first invariant of contact manifolds -- with or without…
We give a partial characterization of bordered Floer homology in terms of sutured Floer homology. The bordered algebra and modules are direct sums of certain sutured Floer complexes. The algebra multiplication and algebra action correspond…
We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',\Gamma') into a larger sutured manifold (M,\Gamma), together with a contact structure on M-M'. As an application of…
We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they…
We consider contact elements in the sutured Floer homology of solid tori with longitudinal sutures, as part of the (1+1)-dimensional topological quantum field theory defined by Honda--Kazez--Mati\'{c} in \cite{HKM08}. The $\Z_2$ $SFH$ of…
We define sutured Heegaard diagrams for null-homologous knots in 3-manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a…
We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As…