Twisted K-theory and obstructions against positive scalar curvature metrics

被引：0

作者：

Pennig, Ulrich ^{[1
]}

机构：

[1] Univ Munster, Math Inst, D-48149 Munster, Germany

来源：

JOURNAL OF K-THEORY | 2014年 / 14卷 / 01期

关键词：

enlargeable manifold; index theory; Dirac operator; positive scalar curvature; twisted index obstruction; twisted K-theory; ENLARGEABILITY;

D O I：

10.1017/is014003008jkt259

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We decompose theta(M), the twisted index obstruction to a positive scalar curvature metric for closed oriented manifolds with spin universal cover, into a pairing of a twisted K-homology with a twisted K-theory class and prove that theta(M) does not vanish if M is a closed orientable enlargeable manifold with spin universal cover.

引用

页码：47 / 71

页数：25

共 28 条

[1] [Anonymous], 1983, PUBL MATH I HAUTES E
[2] Atiyah M., 2004, Ukr. Math. Bull, V1, P291
[3] Atiyah M., 2004, LONDON MATH SOC LECT, V308, P5
[4] Blackadar B, 1998, K-theory for operator algebras, volume 5 of Mathematical Sciences Research Institute Publications, V5
[5] Twisted K-theory and K-theory of bundle gerbes
Bouwknegt, P
Carey, AL
Mathai, V
Murray, MK
Stevenson, D
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 228 (01) : 17 - 45
[6] REPRESENTATIONS OF TWISTED GROUP ALGEBRAS
BUSBY, RC
SMITH, HA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 149 (02) : 503 - +
[7] Thom isomorphism and push-forward map in twisted K-theory
Carey, Alan L.
Wang, Bai-Ling
[J]. JOURNAL OF K-THEORY, 2008, 1 (02) : 357 - 393
[8] Donovan P., 1970, Inst. Hautes tudes Sci. Publ. Math, V38, P5, DOI [10.1007/BF02684650, DOI 10.1007/BF02684650]
[9] Bundle gerbes and surface holonomy
Fuchs, Jurgen
Nikolaus, Thomas
Schweigert, Christoph
Waldorf, Konrad
[J]. EUROPEAN CONGRESS OF MATHEMATICS 2008, 2010, : 167 - +
[10] THE CLASSIFICATION OF SIMPLY CONNECTED MANIFOLDS OF POSITIVE SCALAR CURVATURE
GROMOV, M
LAWSON, HB
[J]. ANNALS OF MATHEMATICS, 1980, 111 (03) : 423 - 434

← 1 2 3 →