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.
Formula connects surgeries to Seiberg-Witten invariants.
We prove a gluing formula for the families Seiberg-Witten invariants of families of -manifolds obtained by fibrewise connected sum. Our formula expresses the families Seiberg-Witten invariants of such a connected sum family in terms of the ordinary Seiberg-Witten invariants of one of the summands, under certain assu…
In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold. The first question we consider is whether the Seiberg-Witten invariants depend on…
We show how the families Seiberg-Witten invariants of a family of smooth -manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families Seiberg-Witten invariants. We give a formula for the Steenrod squares of the fami…
Formula calculates Seiberg-Witten invariants after surgery.
Researchers compute mod 2 Seiberg-Witten invariants for spin structures and families.
Sum formula for relative Seiberg-Witten invariants in 4-manifolds.
We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relat…
In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along…
New connections found between knot invariants and Rozansky-Witten theory.
Proves simple type conjecture for mod 2 Seiberg-Witten invariants.
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, …
Study of Seiberg-Witten invariants for 4-manifolds with group actions.
We compute the Dijkgraaf-Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf-Witten invariants of surfaces of positive genus are positive integers.
The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its relation to the integer valued Seiberg-Witten invariant.
We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works directly on the Donaldson-Witten and Seiberg-Witten moduli spaces. We give a for…
Revisits Vafa-Witten theory, deriving new invariants and homologies.
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.
This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable cohomotopy invariants to Seiberg-Witten invariants without restriction on Betti numbers.…
We investigate Seiberg-Witten theory in the presence of real structures. Certain conditions are obtained so that integer valued real Seiberg-Witten invariants can be defined. In general we study properties of the real Seiberg-Witten projection map from the point of view of Fredholm map degrees.
In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular curves on algebraic surfaces. We first give a topological derivation of the formula by using family index theorem. Then we define the algebrai…
This paper calculates Dijkgraaf-Witten invariants from Chern classes.
New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on compact 4-manifolds of constant negative sectional curvature.
Proves a specific knot is not smoothly slice using real invariants.
Computes Vafa-Witten invariants of 3-manifolds.
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 these invariants give different flavors of Seiberg-Witten Floer homology. We also …
A formula is given which computes the Seiberg-Witten invariant of a 3-orbifold from the invariant of the underlying manifold. As an application, we derive a formula for the Seiberg-Witten invariant of a non-Kähler complex surface, which was originally due to O. Biquard \cite{Biq} and S.R. Williams \cite{W} independentl…
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the symplectic side, we prove that both points of view give the same results. A similar stat…
Paper shows Seiberg-Witten invariants vanish for Davis hyperbolic 4-manifold.
Geometric techniques reveal new insights into Gromov-Witten invariants.
Proves a general connected sum formula for families Seiberg-Witten invariants.
Homological blocks match Witten-Reshetikhin-Turaev invariants for Seifert fibered 3-spheres.
Develops invariants for webs and foams using Seiberg-Witten theory.
We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements of the usual Seiberg-Witten and Ozsvath-Szabo invariants. We…
Proves a formula for a special invariant of 4-manifolds.
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. This generalization is used…
We prove a gluing formula for Seiberg--Witten invariants which describes in particular the behaviour of the invariant under blow-up and rational blow-down.
Paper extends Miyazawa's construction to more 4-manifolds, finding exotic involutions and embeddings.
We prove that the Seiberg-Witten invariants of a rational homology sphere are determined in a very explicit fashion by the Casson-Walker invariant and the Reidemeister torsion
Proof confirms Witten's conjecture for a class of 3-spheres.
We derive an explicit formula for the Witten-Reshetikhin-Turaev SO(3)-invariants of lens spaces. We use the representation of the mapping class group of the torus corresponding to the Witten-Reshetikhin-Turaev SO(3)-TQFT to give such formula.
Study counts hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants up to volume .
New invariant for links in 3-sphere computed and computed using diagrams.
Witten's conjecture suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. A higher rank version of the Donaldson invariants was introduced by Kronheimer. Before even having been defined, the physicists Mariño and…
In this paper, we study relations among known universal equations for Gromov-Witten invariants at genus 1 and 2.
New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.
In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with . In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For every Kähler surface with and =0, these invariants are non-trivial for …