Toeplitz operators and the Roe–Higson type index theorem

  • Tatsuki Seto

    Nagoya University, Japan

Abstract

Let be a complete Riemannian manifold and assume that is partitioned by a hypersurface . In this paper we introduce a novel class of functions on noncompact manifolds, which is slightly larger than the algebra of Higson functions. Out of that belongs to we construct an index class Ind in -group of the Roe algebra of by using the Kasparov product. It is supposed to be a counterpart of Roe's odd index class. We finally prove that Connes' pairing of and Roe's cyclic -cocycle is equal to the Fredholm index of a Toeplitz operator on . This is an extension of the Roe–Higson index theorem to even-dimensional partitioned manifolds.

Cite this article

Tatsuki Seto, Toeplitz operators and the Roe–Higson type index theorem. J. Noncommut. Geom. 12 (2018), no. 2, pp. 637–670

DOI 10.4171/JNCG/287