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Article overview
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Chern-Weil forms and abstract homotopy theory | | Daniel S. Freed
; Michael J. Hopkins
; | | Date: |
25 Jan 2013 | | Abstract: | We prove that Chern-Weil forms are the only natural differential forms
associated to a connection on a principal G-bundle. We use the homotopy theory
of simplicial sheaves on smooth manifolds to formulate the theorem and set up
the proof. Other arguments come from classical invariant theory. We identify
the Weil algebra as the de Rham complex of a specific simplicial sheaf, and
similarly give a new interpretation of the Weil model in equivariant de Rham
theory. There is an appendix proving a general theorem about set-theoretic
transformations of polynomial functors. This paper is dedicated to the memory
of Dan Quillen. | | Source: | arXiv, 1301.5959 | | Services: | Forum | Review | PDF | Favorites | |
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