L2 torsion without the determinant class condition and extended L2 cohomology

Maxim Braverman*, Alan Carey, Michael Farber, Varghese Mathai

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)

    Abstract

    We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L 2 cohomology. Under the determinant class assumption the L 2 torsions of this paper specialize to the invariants studied in our previous work [6]. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler [3] we obtain a Cheeger-Müller type theorem stating the equality between the combinatorial and the analytic L2 torsions.

    Original languageEnglish
    Pages (from-to)421-462
    Number of pages42
    JournalCommunications in Contemporary Mathematics
    Volume7
    Issue number4
    DOIs
    Publication statusPublished - Aug 2005

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