# Torus bundles and the group cohomology of GL(N,Z)

@article{Bismut1995TorusBA, title={Torus bundles and the group cohomology of GL(N,Z)}, author={Jean-Michel Bismut and John Lott}, journal={arXiv: Differential Geometry}, year={1995} }

We prove the vanishing of a certain characteristic class of flat vector bundles when the structure groups of the bundles are contained in GL(N,Z). We do so by explicitly writing the characteristic class as an exact form on the base of the bundle.

## 11 Citations

### Complex Analytic Torsion Forms for Torus Fibrations and Moduli Spaces

- Mathematics
- 2000

We construct analytic torsion forms for line bundles on holomorphic fibrations by tori, which are not necessarily Kahler fibrations. This is done by double transgressing the top Chern class. The…

### TWISTED COCHAINS AND HIGHER TORSION

- Mathematics
- 2002

This paper gives a short summary of the central role played by Ed Brown’s “twisted cochains” in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a…

### TWISTING COCHAINS AND HIGHER TORSION

- Mathematics
- 2002

This paper gives a short summary of the central role played by Ed Brown's "twisting cochains" in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a…

### Computations in formal symplectic geometry and characteristic classes of moduli spaces

- Mathematics
- 2015

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain…

### TWISTING COCHAINS AND HIGHER TORSION 091104

- Mathematics
- 2009

This paper gives a short summary of the central role played by Ed Brown’s “twisting cochains” in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a…

### Computations in formal symplectic geometry

- Mathematics
- 2015

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain…

### Higher Torsion Invariants in Differential Topology and Algebraic K-Theory

- Mathematics
- 2006

The purpose of this Arbeitsgemeinschaft was to study and—as far as possible—compare three generalisations of the classical Franz-Reidemeister torsion to families E → B of manifolds. Dwyer, Weiss and…

### Secondary characteristic classes for subgroups of automorphism groups of free groups

- Mathematics
- 2015

By analyzing how the Borel regulator classes vanish on various groups related to $\mathrm{GL}(n,\mathrm{Z})$, we define three series of secondary characteristic classes for subgroups of automorphism…

### The mathematical work of Jean-Michel Bismut: a brief summary

- 2019

© Société mathématique de France, 2009, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les…

### Local index theory and the Riemann–Roch–Grothendieck theorem for complex flat vector bundles

- MathematicsJournal of Topology and Analysis
- 2018

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…

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