A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture

被引：46
作者：
Schick, T [1 ]
机构：
[1] Univ Munster, Fachbereich Math, D-48149 Munster, Germany
来源：
TOPOLOGY | 1998年 / 37卷 / 06期
关键词：
D O I：
10.1016/S0040-9383(97)00082-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Doing surgery on the 5-torus, we construct a five-dimensional closed spin-manifold M with pi(1)(M) congruent to Z(4) x Z/3, so that the index invariant in the KO-theory of the reduced C*-algebra of pi(1)(M) is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifold cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov-Lawson-Rosenberg conjecture. (C) 1998 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：1165 / 1168
页数：4
相关论文
共 18 条
[1]  
BOTVINNIK BI, UNPUB GROMOVLAWSONRO
[2]  
Federer H., 1969, GRUNDLEHREN MATH WIS, V153
[3]  
Gromov M., 1983, PUBL MATH I HAUTES E, V58, P83
[4]   HARMONIC SPINORS [J].
HITCHIN, N .
ADVANCES IN MATHEMATICS, 1974, 14 (01) :1-55
[5]  
JOACHIM M, 1997, THESIS U NOTRE DAME
[6]   POSITIVE SCALAR CURVATURE AND PERIODIC FUNDAMENTAL-GROUPS [J].
KWASIK, S ;
SCHULTZ, R .
COMMENTARII MATHEMATICI HELVETICI, 1990, 65 (02) :271-286
[7]  
LICHNEROWICZ A, 1963, CR HEBD ACAD SCI, V257, P7
[8]  
Morgan F., 1988, Geometric Measure Theory: A Beginner's Guide
[9]   C-STAR-ALGEBRAS, POSITIVE SCALAR CURVATURE, AND THE NOVIKOV-CONJECTURE .3. [J].
ROSENBERG, J .
TOPOLOGY, 1986, 25 (03) :319-336
[10]  
Rosenberg J., 1995, ECH CENTENNIAL BOSTO, V181, P405
12