Direct image for multiplicative and relative K-theories from transgression of the families index theorem, part 3

2008/04/04 by Alain Berthomieu, Berthomieu, Alain
Mathematics · #14F05 #19E20 #57R20 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:14F05 #msc:19E20 #msc:57R20

paper · pdf · doi:10.48550/arxiv.0804.0728

arxiv created 2008/04/04 · openalex publication_date 2008/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the final part of the work started in math.DG/0611281 and math.DG/0703916. Here the question of double fibration ois adressed both for relative k-theory and free multiplicative K-theory. In the case of relative and ``nonfree'' multiplicative K-theory, the direct image is proved to be functorial for double submersions.

Related

• Direct image for multiplicative and relative K-theories from transgression of the families index theorem, part 2
• Direct image for multiplicative and relative K-theories from transgression of the families index theorem, part 1
• Fibration theorem for Waldhausen K-theory
• Multiplicativity in Mandell's Inverse K-theory
• A stable rank filtration on direct sum K-theory