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 on symmetric operators on non-compact manifolds, focusing on their index modulo 2.
Formulates Index III lemma and Rauch III theorem with applications.
Proves a lattice version of the Atiyah-Singer index theorem.
Explain Arnold's proof of the Morse index theorem using Maslov index.
We give a short proof of the Morse index theorem for geodesics in semi-Riemannian manifolds by using K-theory. This makes the Morse index theorem reminiscent of the Atiyah-Singer index theorem for families of selfadjoint elliptic operators.
Researchers prove an equivariant index theorem on Euclidean space.
Extends a theorem for first-order elliptic operators on manifolds.
In this paper, we prove a local equivariant index theorem for sub-signature operators which generalizes the Zhang's index theorem for sub-signature operators.
The paper proves an index theorem for loop spaces of compact manifolds.
Proves an equivariant version of index theorem for geometric families.
We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our theorem with a classical result of Salamon and Zehnder. Finally, we use the index theo…
We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin manifolds. The analytic index is the reduced invariant of (twisted) Dirac operators and the topological index is defined through -theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-o…
Extends index theorem to domain walls with discontinuous Riemannian connections.
In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's -index theorem. This note also contains an example of Heisenberg differential operators with non-trivial -index.
Atiyah-Singer theorem links math fields, predicts topological insights.
Massive fermions help understand index theorems without chiral symmetry.
A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …
Proves Morse index theorem for geodesics in conic Finsler manifolds.
The paper proves index theorems for graph-based optimal control problems.
Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.
Absolute index theorem for warped product manifolds.
Paper provides a rigorous proof of the index theorem for economists.
In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.
In this paper, we extend Roe's cyclic -cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are generalizations of index theorems on partitioned manifolds. One of these theorems is a variant of [M. Karami-A.H.S. Sadegh-M.E. Zadeh, arXiv:…
In this paper we show an index theorem for gerbes
In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary.
In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss the odd dimensional counterparts of the above results. In particular, we describe…
Higher index theorem for Dirac operators on finite-volume spaces.
Researchers construct an index map for contact manifolds using K-theory.
An expression is found for the -index of a Dirac operator coupled to a connection on a vector bundle over . Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection i…
We give a superconnection proof of Connes' index theorem for proper cocompact actions of etale groupoids. This includes Connes' general foliation index theorem for foliations with Hausdorff holonomy groupoid.
In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.
Proves a theorem for mechanical systems with reflections.
This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-bro…
Proves super-version of index theorem from algebraic cobordism invariants.
We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any manifold of bounded geometry. This local formula incorporates the uniform estimates …
Paper extends index theorem to odd-dimensional manifolds with even-dimensional boundaries.
In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.
Two proofs of Melrose-Piazza theorem on spectral sections.
The index theorem connects anomalies on a domain wall to global integrals.
In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
Researchers extend Gamma index theorem to non-compact spacetimes.
We present an index theorem for certain hypoelliptic differential operators on foliated manifolds. Our proof is a development of Alain Connes tangent groupoid proof of the Atiyah-Singer index theorem. The paper is largely self-contained.
Global Morse index theorem applied to Jacobi fields on CMC surfaces.
Paper develops formulas and theorems in Hermitian geometry.
In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.
This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem for geometric operators, as well as the nonlocal invariants (the eta invariant, the determinant of the Laplacian/analytic …