UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Transgressions of the Euler class and Eisenstein cohomology of GLN(Z)

Garcia Martinez, L; Bergeron, N; Charollois, P; (2020) Transgressions of the Euler class and Eisenstein cohomology of GLN(Z). Japanese Journal of Mathematics 10.1007/s11537-019-1822-6. (In press). Green open access

[img]
Preview
Text
Takagi-final-JJM1822.pdf - Accepted version

Download (564kB) | Preview

Abstract

These notes were written to be distributed to the audience of the first author’s Takagi Lectures delivered June 23, 2018. These are based on a work-in-progress that is part of a collaborative project that also involves Akshay Venkatesh. In this work-in-progress we give a new construction of some Eisenstein classes for GLN (Z) that were first considered by Nori [41] and Sczech [44]. The starting point of this construction is a theorem of Sullivan on the vanishing of the Euler class of SLN (Z) vector bundles and the explicit transgression of this Euler class by Bismut and Cheeger. Their proof indeed produces a universal form that can be thought of as a kernel for a regularized theta lift for the reductive dual pair (GLN, GL1). This suggests looking to reductive dual pairs (GLN, GLk) with k ≥ 1 for possible generalizations of the Eisenstein cocycle. This leads to fascinating lifts that relate the geometry/topology world of real arithmetic locally symmetric spaces to the arithmetic world of modular forms. In these notes we do not deal with the most general cases and put a lot of emphasis on various examples that are often classical.

Type: Article
Title: Transgressions of the Euler class and Eisenstein cohomology of GLN(Z)
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11537-019-1822-6
Publisher version: https://doi.org/10.1007/s11537-019-1822-6
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10086959
Downloads since deposit
5Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item