Index theory for basic Dirac operators on Riemannian foliations

被引：0
作者：
Bruening, Jochen [1 ]
Kamber, Franz W. [2 ]
Richardson, Ken [3 ]
机构：
[1] Humboldt Univ, Inst Math, Unter den Linden 6, D-10099 Berlin, Germany
[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA
[3] Texas Christian Univ, Dept Math, Ft Worth, TX 76129 USA
来源：
NONCOMMUTATIVE GEOMETRY AND GLOBAL ANALYSIS | 2011年 / 546卷
关键词：
foliation; basic; index; transversally elliptic; ELLIPTIC-OPERATORS; SPECTRAL ASYMMETRY; V-MANIFOLDS; GEOMETRY; DUALITY; COMPACT; ASYMPTOTICS; EIGENVALUE; FLOWS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.
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页码：39 / +
页数：4
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