K-homology and index theory on contact manifolds

• 成果类型: Article
• 署名作者: Baum, Paul F.; van Erp, Erik
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Dartmouth College
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0114-5
• 发表日期: 2014
• 页码: 1-48
• 关键词: subelliptic operators; FORMULA

摘要

This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus. The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of Atiyah-Singer type to non-elliptic Fredholm operators.