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Logarithm of differential forms and regularization of volume forms. (English) Zbl 1034.58003

Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 8th international conference, Opava, Czech Republic, August 27–31, 2001. Opava: Silesian University at Opava (ISBN 80-7248-166-5/hbk). Math. Publ. (Opava) 3, 165-174 (2001).
The author uses the logarithm of derivation and defines the logarithm of a differential form. Next he defines fractional order differential forms on a flat space. The regularized volume form on a flat infinite dimensional space is also defined. By using fractional order differential forms and applying a noncommutative connection, it is shown that the regularized volume form can be defined on a mapping space if its string class vanishes.
For the entire collection see [Zbl 1008.00021].

MSC:

58A10 Differential forms in global analysis
58J52 Determinants and determinant bundles, analytic torsion
26A33 Fractional derivatives and integrals
81R60 Noncommutative geometry in quantum theory
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