An equivariant index for proper actions I

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• 作者：Peter Hochs^a ; ^{peter.hochs@adelaide.edu.au" class="auth_mail" title="E-mail the corresponding author} ; Yanli Song^b ; ^{song@math.dartmouth.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Equivariant index ; Proper group action ; K-Homology ; Crossed product C⁎C⁎-algebra
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：272
• 期：2
• 页码：661-704
• 全文大小：643 K

文摘

Equivariant indices, taking values in group-theoretic objects, have previously been defined in cases where either the group acting or the orbit space of the action is compact. In this paper, we define 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 explore some properties and applications of this index.