Applying geometric K-cycles to fractional indices
Journal article, 2017

© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim A geometric model for twisted K-homology is introduced. It is modeled after the Mathai–Melrose–Singer fractional analytic index theorem in the same way as the Baum–Douglas model of K-homology was modeled after the Atiyah–Singer index theorem. A natural transformation from twisted geometric K-homology to the new geometric model is constructed. The analytic assembly mapping to analytic twisted K-homology in this model is an isomorphism for torsion twists on a finite CW-complex. For a general twist on a smooth manifold the analytic assembly mapping is a surjection. Beyond the aforementioned fractional invariants, we study T-duality for geometric cycles.


geometric K-homology

fractional analytic index

twisted K-homology

Primary: 19L50

Secondary: 55N20

index theory


R.J. Deeley

Magnus C H T Goffeng

Chalmers, Mathematical Sciences

University of Gothenburg

Mathematische Nachrichten

0025-584X (ISSN) 1522-2616 (eISSN)

Vol. 290 14-15 2207-2233


Basic sciences

Subject Categories


Mathematical Analysis



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