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.
New Witten rigidity theorems for elliptic genus in various dimensions.
New rigidity theorems for spin^c manifolds using modular invariance.
We establish the family rigidity and vanishing theorems on the equivariant -theory level for the Witten type operators on String manifolds introduced by Chen-Han-Zhang.
We prove integral rigidity for Seiberg-Witten invariants of 4-manifolds with specific hypersurfaces.
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd Chern classes for cocycles in odd -theory. Moreover we discover that in odd dimen…
This paper extends Witten's holomorphic Morse inequalities to singular spaces.
In this paper the Gromov-Witten invariants on a class of noncompact symplectic manifolds are defined by combining Ruan-Tian's method with that of McDuff-Salamon. The main point of the arguments is to introduce a method dealing with the transversality problems in the case of noncompact manifolds. Moreover, the technique…
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and tota…
New rigidity theorems for spin fill-ins with non-negative scalar curvature.
In this paper, we first prove a local family version of the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, then we extend the famous Witten's rigidity Theorems to the family case. Several family vanishing theorems for elliptic genera are also proved.
In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…
The paper proves properties of a specific Seiberg-Witten equation over 3-manifolds.
Proves rigidity of SU(2) and SO(3) quantum representations at prime levels.
Quantum representations of mapping class groups are locally rigid at prime levels.
In this paper, we construct for the first time, the Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group and prove vanishing and rigidity results that generalise known results for compact group actions on compact manifolds. We also compute our genera f…
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result and a positive mass theorem for asymptotically hyperbolic manifol…
In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds equipped with -super Perelman Ricci flow. We establish the -entropy formula for the heat equation of the Witten Laplacian and prove a …
In this paper, we first establish an -equivariant index theorem for Spin Dirac operators on manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198}, we extend Witten's rigidity theorem to the case of Spin manif…
Paper proves rigidity for spin bands with specific conditions.
Formula derived for mass of almost Kähler manifolds, extending previous results.
Using the new diffeomorphism invariants of Seiberg and Witten, a uniqueness theorem is proved for Einstein metrics on compact quotients of irreducible 4-dimensional symmetric spaces of non-compact type. The proof also yields a Riemannian version of the Miyaoka-Yau inequality.
We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.
Paper introduces a new geometric homology theory and applies it to Gromov-Witten theory.
Elliptic bouquets defined for spin manifolds with circular actions.
Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asympto…
We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on . This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimension…
Kawakubo and Uchida showed that, if a closed oriented -dimensional manifold admits a semi-free circle action such that the dimension of the fixed point set is less than , then the signature of vanishes. In this note, by using -signature theorem and the rigidity of the signature operator, we generaliz…
Compact proof for Brown-York mass positivity and rigidity in flat and spherical spaces.
Recently L. Nicolaescu and the author formulated a conjecture which relates the geometric genus of a complex analytic normal surface singularity (whose link is a rational homology sphere) with the Seiberg-Witten invariant of associated with the ``canonical'' structure of . Since the Seiberg-Witten t…
This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: …
Using a hyperKähler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural family of immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and study how they …
In this paper, we prove the concavity of the Shannon entropy power for the heat equation associated with the Laplacian or the Witten Laplacian on complete Riemannian manifolds with suitable curvature-dimension condition and on compact super Ricci flows. Under suitable curvature-dimension condition, we prove that the ri…
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
We initiate here the study of Gromov-Witten theory of locally conformally symplectic manifolds or $\lcs$ manifolds, $\lcsm$'s for short, which are a natural generalization of both contact and symplectic manifolds. We find that the main new phenomenon (relative to the symplectic case) is the potential existence of holom…
Initial data with zero mass must be in pp-wave spacetimes.
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…
Formula connects surgeries to Seiberg-Witten invariants.
Computes spectral Einstein functional for Witten deformation on even-dimensional spin manifolds.
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 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…
Simple perturbation of Vafa-Witten equations leads to transversality.
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…
Lectures on linearized Kapustin-Witten equations on half-line.
Formula calculates Seiberg-Witten invariants after surgery.
Study Witten deformation on noncompact manifolds with bounded geometry.
The paper studies eigenfunctions and nodal sets of the Witten-Laplacian.
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.
The paper proves formulas and theorems for J-Witten deformation on specific manifolds.