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On relative cohomology in Lie theory

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Salazar,  María Amelia
Max Planck Institute for Mathematics, Max Planck Society;

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2407.00169.pdf
(Preprint), 413KB

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Citation

Salazar, M. A. (submitted). On relative cohomology in Lie theory.


Cite as: https://hdl.handle.net/21.11116/0000-000F-821E-D
Abstract
Motivated by our attempt to understand characteristic classes of Lie groupoids and geometric structures, we are brought back to the fundamentals of the cohomology theories of Lie groupoids and algebroids. One element that was missing in the literature was the notion of relative cohomology in this setting. The main aim of this paper is to develop the structural theory of this notion, the relation between the relative cohomology of groupoids and that of algebroids via van Est maps, and to indicate how it can be used to provide an intrinsic definition of characteristic classes.