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.
Proves a theorem for complex flat vector bundles using differential forms.
Develops equivariant Chern characters for coherent sheaves with group actions.
Study of orbifold Chern character using superconnections.
Paper constructs Chern character for coherent sheaves.
The purpose of this paper is to give a proof of the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an application of the local family index theorem for a perturbed twisted spin Dirac op…
Develops a new index theory for odd Z/kZ K-theory.
We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott. Then we consider the direct image of a fiberwise holomorphic vector bundle, which is a flat vector bundle on the base. We gi…
We present a new proof, as well as a extension, of the Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of -invariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott a…
We survey the Hirzebruch signature theorem as a special case of the Atiyah-Singer index theorem. The family version of the Atiyah-Singer index theorem in the form of the Riemann-Roch-Grothendieck-Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of ellipti…
Paper extends variational formula for Bismut-Cheeger eta form, proving key theorems in K-theory.
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps which, for smooth connections on and , establishes formulas of the type $$ φ\ = \ \text{\rm Res}_φΣ…
In this article we study the Quillen norm on the determinant line bundle associated with a family of complex curves with cusps, which admit singular fibers. More precisely, we fix a family of complex curves , which admit at most double-point singularities. Let be a holomorphic Hermitian vector bu…