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.
The paper compares two torsion invariants in complex vector bundles.
Analytic surgery and gluing formula for torsion forms in fiber bundles.
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 give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.
Equivalence proven between two torsion invariants for flat vector bundles.
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …
In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that the metrics have product structures near the cutting hypersurface.
For a complex flat vector bundle over a fibered manifold, we consider the 1-parameter family of certain deformed sub-signature operators introduced by Ma-Zhang. We compute the adiabatic limit of the Bismut-Freed connection associated to this family and show that the Bismut-Lott analytic torsion form shows up naturally …
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 consider a closed odd-dimensional oriented manifold together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre over the manifold of all Riemannian metrics on . It has a natural flat connection and a vertical Riemannian metric. The higher analytic torsion form …
Formula connects analytic torsion forms of fibration and its pieces.