Families index for manifolds with boundary, superconnections, and cones. I. Families of manifolds with boundary and Dirac operators

Jean Michel Bismut, Jeff Cheeger

Research output: Contribution to journalReview articlepeer-review

Abstract

This is Part I of a work, in which we establish a formula for the Chern character of a family of Dirac operators of Atiyah-Patodi-Singer on even-dimensional manifolds with boundary. The key tools are the superconnections of Quillen, the cone method, and the Levi-Civita superconnection. In this Part I, we construct a family of Dirac operators on manifolds with boundary and we introduce the corresponding Levi-Civita superconnections.

Original languageEnglish (US)
Pages (from-to)313-363
Number of pages51
JournalJournal of Functional Analysis
Volume89
Issue number2
DOIs
StatePublished - Mar 15 1990

ASJC Scopus subject areas

  • Analysis

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