Let $\mb{X}\,=\,[X_1\rra X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mc{H}\,\subset \,T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution $\mc{H}$ is integrable, we define a version of de Rham cohomology for the pair $(\mb{X},\, \mc{H})$, and we study connections on principal $G$-bundles over $(\mb{X},\, \mc{H})$ in terms of the associated Atiyah sequence of vector bundles. We also discuss associated constructions for differentiable stacks. Finally, we develop the corresponding Chern-Weil theory and describe characteristic classes of principal $G$-bundles over a pair $(\mb{X},\, \mc{H})$.
Connections on Lie groupoids and Chern–Weil theory
Neumann
2024-01-01
Abstract
Let $\mb{X}\,=\,[X_1\rra X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mc{H}\,\subset \,T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution $\mc{H}$ is integrable, we define a version of de Rham cohomology for the pair $(\mb{X},\, \mc{H})$, and we study connections on principal $G$-bundles over $(\mb{X},\, \mc{H})$ in terms of the associated Atiyah sequence of vector bundles. We also discuss associated constructions for differentiable stacks. Finally, we develop the corresponding Chern-Weil theory and describe characteristic classes of principal $G$-bundles over a pair $(\mb{X},\, \mc{H})$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
