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Secondary theories for simplicial manifolds and classifying spaces

Marcello Felisatti and Frank Neumann

Geometry & Topology Monographs 11 (2007) 33–58

DOI: 10.2140/gtm.2007.11.33

arXiv: 0903.4870

Abstract

We define secondary theories and characteristic classes for simplicial smooth manifolds generalizing Karoubi’s multiplicative K–theory and multiplicative cohomology groups for smooth manifolds.

As a special case we get versions of the groups of differential characters of Cheeger and Simons for simplicial smooth manifolds.

Special examples include classifying spaces of Lie groups and Lie groupoids.

Keywords

multiplicative K–theory, multiplicative cohomology, differential characters, smooth simplicial manifolds, simplicial de Rham theory

Mathematical Subject Classification

Primary: 55N15, 57R19, 57R20

Secondary: 22A22, 55R40, 58A12

References
Publication

Received: 24 March 2005
Revised: 29 June 2005
Accepted: 11 July 2005
Published: 14 November 2007

Authors
Marcello Felisatti
Department of Mathematics
University of Leicester
Leicester
LE1 7RH
UK
Frank Neumann
Department of Mathematics
University of Leicester
Leicester
LE1 7RH
UK