A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study contact structures and sutured monopole Floer homology, computing and deriving formulas.
Paper constructs maps for sutured monopole Floer homology.
Paper generalizes sutured Floer homologies with new algorithms and polytopes.
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 closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, a…
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 Heegaard Floer homology which identifies our invariant with the contact class defi…
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 refinements of these invariants which assign much richer algebraic objects called projecti…
We develop monopole and instanton Floer homology groups for balanced sutured manifolds. Applications include a new proof of Property P for knots.
The paper constructs knot homologies for monopole and instanton theories.
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 the knot Floer homology invariants of Lisca, Ozsváth, Stipsicz, and Szabó. We pr…
Paper proves depth bounds for taut foliations using instanton Floer homology.
Proves properties of instanton knot Floer homology and connected sum formula.
New technique connects instanton Floer homology to Heegaard diagrams for knots and 3-manifolds.
Developed a real sutured Heegaard Floer theory.
Contact gluing maps are shown to be equivalent in sutured Floer homology.
Study links with annuli using sutured Floer homology.
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 corresponds to contact elements in sutured Floer homology. We use this approach t…
Paper classifies Heegaard Floer minimal knots in sutured manifolds.
New homological action on sutured instanton homology defined.
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 part is a construction of Heegaard Floer homology as a special, and slightly mod…
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 contain. In particular, we use sutured Floer homology to distinguish two non-isotopi…
Sutured instanton homology uses Heegaard diagrams to bound homology dimensions.
Link Floer homology detects split links.
Proves a new skein exact triangle for real monopole Floer homology.
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 much of the formal structure relating the various versions of Heegaard Floer ho…
Framework extends sutured manifold invariants to pairs with torus boundaries.
This paper studies knots in sutured manifolds achieving minimum instanton homology rank.
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 boundary -- defined in the instanton Floer setting. We prove that our invariant vani…
It has been a central open problem in Heegaard Floer theory whether cobordisms of links induce homomorphisms on the associated link Floer homology groups. We provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds, and showing that such a cobordism induces a map on sutured F…
New instanton Floer homology for sutured manifolds with tangles defined.
In this paper we find a family of knots with trivial Alexander polynomial, and construct two non-isotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study the sutured Floer homology invariants of the sutured manifolds obtained by cutting the knot complements along the Seifer…
Abstract TQFT for sutured manifolds using Floer homology.
We exhibit the first example of a knot in the three-sphere with a pair of minimal genus Seifert surfaces that can be distinguished using the sutured Floer homology of their complementary manifolds together with the Spin^c-grading. This answers a question of Juhász. More precisely, we show that the Euler characteristic …
The paper defines contact invariants in bordered Floer homology.
We describe an invariant of a contact 3-manifold with convex boundary as an element of Juhász's sutured Floer homology. Our invariant generalizes the contact invariant in Heegaard Floer homology in the closed case, due to Ozsváth and Szabó. This version has some clarifications and new figures.
We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',Γ') into a larger sutured manifold (M,Γ), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its…
Paper studies spectral invariants and monopole Floer homology for rational homology three-spheres.
Research provides obstructions to Stein fillings of certain rational homology spheres.
We give an explicit construction of the Honda--Kazez--Matić gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link F…
Study SOLV geometry using monopole Floer homology.
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show…
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 to a new gluing map on SFH. It is defined algebraically, and is a special case o…
We show that the sutured Floer homology of a sutured 3-manifold of the form can be expressed as the homology of a string-type complex, generated by certain sets of curves on and with a differential given by resolving crossings. We also give some generalisations of this isomor…
Develops invariants for webs and foams using Seiberg-Witten theory.
Study Seiberg-Witten theory on manifolds with codimension-3 foliations.
Unified tau invariants in instanton and monopole Floer theories.
Third paper in series defines monopole Floer homology and gluing theorem for 3-manifolds.
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 homology can be calculated in terms of the Heegaard Floer/monopole Floer lattice compl…
Innovative contact invariant derived from Heegaard Floer homology.