SMOOTH K-THEORY

By U. Bunke, Thomas Schick. 2007

93 citations recorded by the source corpus.

In this paper we consider smooth extensions of cohomology theo- ries. In particular we construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion p: W → B and define the associated push-forward ˆ p! : ˆ K(W) → ˆ K(B). We show that the push-forward has the expected properties as functoriality, compatibility with pull-back diagrams, projection formula and a bordism formula. We construct a multiplicative lift of the Chern character ˆ ch : ˆ K(B) → ˆ H(B, Q),

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/db817256e780ac787dc715cea3ab8456c73e3cde

Citations in the corpus

• Structured Vector Bundles Define Differential K-Theory (2008, unknown): “This paper grew out of the effort to construct a simple geometric model for differential K-theory, the fibre product of usual K-theory with closed differential forms, [4],[5],[6].”
• Differential cohomology theories as sheaves of spectra (2013, unknown): “This definition is justified by the fact, that if R is a commutative ring and P (R) is the symmetric monoidal category of finitely generated projective R-modules with respect to the direct sum, then KR := K(P (R)) is a connective spectrum which represents Quillen’s algebraic K-theory of R.”