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.
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.…
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.
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.
Proves a specific knot is not smoothly slice using real invariants.
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.
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…
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 …
In this paper, we study relations among known universal equations for Gromov-Witten invariants at genus 1 and 2.