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.
Researchers construct an index map for contact manifolds using K-theory.
The abstract discusses connecting quantum mechanics and algebraic index theories.
We discuss some aspects of index and secondary index theory for flat bundles with duality. This theory was first developed by J. Lott. Our main purpose in the present paper is to provide a modification with better functorial properties.
Extends index theory results to manifolds with boundaries.
Unified geometric perspectives on PDEs, torsion invariants, and moduli theory.
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
Proves a lattice version of the Atiyah-Singer index theorem.
Proves super-version of index theorem from algebraic cobordism invariants.
Local index formula for Lorentzian Dirac operators on spacetimes.
The paper explores the index theory of sub-Laplacians on higher nilpotent Carnot manifolds.
Develops a new index theory for odd Z/kZ K-theory.
We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differenti…
Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.
Refined 3D index uses surgery and gradings to distinguish 3-manifolds.
Paper extends index theorem to odd-dimensional manifolds with even-dimensional boundaries.
Paper introduces danceability index as a new bridge index definition.
Constructs index for elliptic operators using rapidly decaying kernels.
The paper explores index theory for Dirac operators to understand scalar curvature properties.
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are su…
The notion of pseudo-differential operators with coefficients in a continuous trace algebra over a manifold are introduced and their index theory is studied. The algebra of principal symbols in this calculus provides an abstract Poincaré dual to the continuous trace algebra. Index formulas for pseudo-differential opera…
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is the equality of these two notions of index when the twisting class is in the torsi…
Develops obstruction theory for a specific 4-manifold index.
This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up ("K-homology and index theory II: Elliptic Operators") was written to clear up basic points about index theory that a…
Unified proof of knot unknotting bounds using Ma-Qiu index.
We compute the index of the real Cauchy-Riemann operator defined in FJRW theory in case of the smooth metric. For the cylindrical metric, we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev space.
Constructs a model for differential KO-theory using Clifford modules.
We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such …
This is an expository paper which gives a proof of the Atiyah-Singer index theorem for elliptic operators. Specifcally, we compute the geometric K-cycle that corresponds to the analytic K-cycle determined by the operator. This paper and its companion ("K-homology and index theory II: Dirac Operators") was written to cl…
An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic…
This study explores the index theory of Heisenberg elliptic and transversally Heisenberg elliptic operators using -theory.
Study hypoelliptic operators on Carnot manifolds, extending index theory results.
Abstract machinery finds obstructions to uniform positive scalar curvature.
Extends width estimates to family case using index theory.
Study elliptic boundary problems on surfaces, deriving index formulas.
Study index theory on Lie group homogeneous spaces using topological and analytic methods.
Explores new perspectives in transverse index theory for Lie group actions.
Paper constructs a transfer map for codimension 2 submanifolds in higher index theory.
Shelstad's character identity is an equality between sums of characters of tempered representations in corresponding -packets of two real, semisimple, linear, algebraic groups that are inner forms to each other. We reconstruct this character identity in the case of the discrete series, using index theory of elliptic…
The study analyzes spectral asymmetry and index theory on manifolds with generalized hyperbolic cusps.
New index formulae derived for operators on boundary groupoids.
The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over -algebras of continuous functions to obtain a meaningful index. Inspired by work by Roe, we t…
In this note we prove some results in flat and differential -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential -theory and Freed-Lott diff…
This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.
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 …
In this paper, we study the family index of a family of spin manifolds. In particular, we discuss to which extend the real index (of the Dirac operator of the real spinor bundle if the fiber dimension is divisible by 8) which can be defined in this case contains extra information over the complex index (the index of it…
The paper proves an index theorem for loop spaces of compact manifolds.
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.
Lattice formulation captures Atiyah-Patodi-Singer index.