De Rham theory and cocycles of cubical sets from smooth quandles (Q2312753)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | De Rham theory and cocycles of cubical sets from smooth quandles |
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De Rham theory and cocycles of cubical sets from smooth quandles (English)
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17 July 2019
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Given a quandle \(X\) (a quandle is a space with a binary operation that satisfies certain laws akin to those obeyed by conjugation on a group) it is possible to form a classifying space \(BX\) as a cubical set. This paper considers the case where the quandle \(X\) has a manifold structure. The author shows a de Rham theorem for \(BX\) and determines the rational cohomology of \(BX\). The author further examines the contrast between the cohomology groups of \(BX\) and \(BX^{\delta}\) where \(X^{\delta}\) denotes the discrete topology on \(X\).
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cubical sets
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quandle
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de Rham theory
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secondary characteristic classes
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invariant theory
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