2012/11/28 by Antti J. Harju, Harju, Antti J.
Mathematics · #19L50 #22A22 #53C08 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1211.6761
openalex publication_date 2012/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a study of twisted K-theory on a product space T \× M. The\ntwisting comes from a decomposable cup product class which applies the\n1-cohomology of T and the 2-cohomology of M. In the case of a topological\nproduct, we give a concrete realization for the gerbe associated to a cup\nproduct characteristic class and use this to realize twisted K1-theory\nelements in terms of supercharge sections in a Fredholm bundle. The\nnontriviality of this construction is proved. Equivariant twisted K-theory and\ngerbes are studied in the product case as well. This part applies Lie groupoid\ntheory. Superconnection formalism is used to provide a construction for\ncharacteristic polynomials which are used to extract information from the\ntwisted K-theory classes.\n