Year: 2025
Type: article
Abstract: The purpose of this paper is to prove that if Y is a compact manifold, if Z is an Anosov vector field on Y, and if F is a flat vector bundle, there is a corresponding canonical nonzero section $$\tau _{\nu }\left( i_{Z}\right) $$ τ ν i Z of the determinant line $$\nu =\det H\left( Y,F\right) $$ ν = det H Y , F . In families, this section is $$C^{1}$$ C 1 with respect to the canonical smooth structure on $$\nu $$ ν . When F is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $$\nu $$ ν .
Authors: Jean-Michel Bismut, Shu Shen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4398762095