An equivariant index for proper actions I

Abstract

Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop an equivariant index without assuming the group or the orbit space to be compact. This allows us to generalise an index of deformed Dirac operators, defined for compact groups by Braverman. In parts II and III of this series, we will explore some properties and applications of this index.

47 pages. The initial version was split into two parts. This is now the first part, the second part is arXiv:1602.02836. The last revision includes corrections after comments from a referee