Homotopy theory of C_∞-algebras and characteristic classes of fiber bundles

2016/05/25 by Hiroshige Kajiura, Kajiura, Hiroshige, Takahiro Matsuyuki +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:18G55 #msc:55R40 #msc:57R20

paper · pdf · doi:10.48550/arxiv.1605.07904

16 pages. New examples have been added. The title has been changed. Typos have been fixed

arxiv created 2019/05/28 · arxiv updated 2019/05/29

Abstract

In this paper we give a Chern-Weil-type construction of characteristic classes of fiber bundles, based on homotopy theory of C-infinity algebras. Our idea is to replace a family of closed manifolds to a family of C-infinity morphisms with family of metrics.

Related

• Obstruction of C_∞-algebra models and characteristic classes
• The Chern-Weil-Lecomte characteristic map for L_∞-algebras
• Characteristic classes of A-infinity algebras
• Smooth Homotopy of Infinite-Dimensional C^∞-Manifolds
• Characteristic classes associated to Q-bundles