Homotopy quantum field theory and the index gerbe

Abstract

Given a family of Dirac operators with vanishing spectral flow we construct a thin-invariant rank-one field theory in the sense of Turner and Willerton arXiv:math.AT/0201116. Our construction of the field theory generalizes the one of the index gerbe by Lott, arXiv:math.DG/0106177, and it also complements the relation between gerbes and thin-invariant rank-one field theories studied in arXive:math.AT/0201116.

9 pages

References in corpus (2)

• Higher-Degree Analogs of the Determinant Line Bundle
• Transgression of the index gerbe