Surgery and harmonic spinors

被引：20

作者：

Ammann, Bernd ^{[2
]}

Dahl, Mattias ^{[1
]}

Humbert, Emmanuel ^{[3
]}

机构：

[1] Kungliga Tekn Hogskolan, Inst Matemat, S-10044 Stockholm, Sweden

[2] Univ Regensburg, NWF I Math, D-93040 Regensburg, Germany

[3] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

来源：

ADVANCES IN MATHEMATICS | 2009年 / 220卷 / 02期

关键词：

Dirac operator; Eigenvalue; Surgery; SIMPLY CONNECTED MANIFOLDS; POSITIVE SCALAR CURVATURE; DIRAC OPERATOR;

D O I：

10.1016/j.aim.2008.09.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M he a compact spin manifold with a chosen spin structure. The Atiyah-Singer index theorem implies that for any Riemannian metric on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and the spin structure. We show that for generic metrics on M this bound is attained. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：523 / 539

页数：17

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