The Chern Character in the Simplicial de Rham Complex
Naoya Suzuki
TL;DR
This paper constructs a cocycle in the simplicial de Rham complex representing the Chern character and proves Brylinski's conjecture, providing a method for local cocycle construction.
Contribution
It introduces a new cocycle in the simplicial de Rham complex representing the Chern character and proves a related conjecture by Brylinski.
Findings
Constructed a cocycle representing the Chern character.
Proved Brylinski's conjecture.
Provided a method for local cocycle construction.
Abstract
On the basis of Dupont's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Chern character. We also prove the related conjecture due to Brylinski. This gives a way to construct a cocycle in a local truncated complex.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research · Advanced Topics in Algebra