The homotopy types of Sp(2)-gauge groups

被引：30

作者：

Theriault, Stephen D. ^{[1
]}

机构：

[1] Univ Aberdeen, Dept Math Sci, Aberdeen AB24 3UE, Scotland

来源：

KYOTO JOURNAL OF MATHEMATICS | 2010年 / 50卷 / 03期

关键词：

GAUGE GROUPS; SAMELSON PRODUCTS; SP(2); SU(3);

D O I：

10.1215/0023608X-2010-005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There are countably many equivalence classes of principal Sp(2)-bundles over S-4 classified by the integer value of the second Chern class. We show that the corresponding gauge groups G(k) have the property that if there is a homotopy equivalence G(k) Gk', then (40, k) = (40, k'), and we prove a partial converse by showing that if (40, k) = (40, k'), then G(k) and G(k)' are homotopy equivalent when localized rationally or at any prime.

引用

页码：591 / 605

页数：15

共 16 条

[1]

[Anonymous], 1963, J MATH KYOTO U

[2] THE YANG-MILLS EQUATIONS OVER RIEMANN SURFACES [J].

ATIYAH, MF ;

BOTT, R .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1983, 308 (1505) :523-615

[3]

Bott R., 1960, COMMENT MATH HELV, V34, P245

[4] Composition methods and homotopy types of the gauge groups of Sp(2) and SU(3) [J].

Choi, Younggi ;

Hirato, Yoshihiro ;

Mimura, Mamoru .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2008, 15 (03) :409-417

[5] Counting homotopy types of gauge groups [J].

Crabb, MC ;

Sutherland, WA .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2000, 81 :747-768

[6] Unstable K1-group and homotopy type of certain gauge groups [J].

Hamanaka, H ;

Kono, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2006, 136 :149-155

[7] Samelson products in Sp(2) [J].

Hamanaka, Hiroaki ;

Kaji, Shizuo ;

Kono, Akira .

TOPOLOGY AND ITS APPLICATIONS, 2008, 155 (11) :1207-1212

[8]

HARPER JR, 2002, GRAD STUDIES MATH, V49

[9] Samelson products of SO(3) and applications [J].

Kamiyama, Yasuhiko ;

Kishimoto, Daisuke ;

Kono, Akira ;

Tsukuda, Shuichi .

GLASGOW MATHEMATICAL JOURNAL, 2007, 49 :405-409

[10] A NOTE ON THE HOMOTOPY TYPE OF CERTAIN GAUGE GROUPS [J].

KONO, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1991, 117 :295-297

← 1 2 →