Coarse homotopy theory and boundary value problems

2018/06/10 by Ulrich Bunke, Bunke, Ulrich
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Metric Geometry (math.MG) #math.DG #math.KT #math.MG

paper · pdf · doi:10.48550/arxiv.1806.03669

22 pages

arxiv created 2018/06/10 · arxiv updated 2018/06/12

Abstract

We provide an interpretation of the APS index theorem of Piazza-Schick and Zeidler in terms of coarse homotopy theory. On the one hand we propose a motivic version of the boundary value problem, the index theorem, and the associated secondary invariants. On the other hand, we discuss in detail how the abstract version is related with classical case for Dirac operators.

Related

• The homotopy classification and the index of boundary value problems for general elliptic operators
• The relative index in coarse index theory and submanifold obstructions to uniform positive scalar curvature
• Coarse indices of twisted operators
• Branched coarse coverings and transfer maps
• Positive curvature, partial vanishing theorems, and coarse indices