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Applying geometric K ‐cycles to fractional indices
Author(s) -
Deeley Robin J.,
Goffeng Magnus
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600039
Subject(s) - mathematics , surjective function , atiyah–singer index theorem , twist , pure mathematics , torsion (gastropod) , isomorphism (crystallography) , homology (biology) , geometry , medicine , biochemistry , crystal structure , chemistry , surgery , gene , crystallography
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 C W ‐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.