We prove an analogue for odd-dimensional manifolds with boundary, in the b-calculus setting, of the higher Atiyah–Patodi–Singer index theorem by Getzler and by Wu, and thus obtain a natural counterpart of the eta invariant for even-dimensional closed manifolds.
Cite this article
Zhizhang Xie, The odd-dimensional analogue of a theorem of Getzler and Wu. J. Noncommut. Geom. 7 (2013), no. 3, pp. 647–676DOI 10.4171/JNCG/130