The homotopy types of SU(4)-gauge groups over S8

被引：5

作者：

Mohammadi, Sajjad ^{[1
]}

Asadi-Golmankhaneh, Mohammad A. ^{[2
]}

机构：

[1] Univ Urmia, Dept Math, POB 5756151818, Orumiyeh, Iran

[2] Univ Urmia, Dept Math, POB 165, Orumiyeh, Iran

来源：

TOPOLOGY AND ITS APPLICATIONS | 2019年 / 266卷

关键词：

Gauge group; Homotopy type; Lie group; Homotopy equivalence; SAMELSON PRODUCTS;

D O I：

10.1016/j.topol.2019.106845

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P-4,P-k be the principal SU(4)-bundle over S-8 with Chern class c(4)(P-4,P-k) = 6k and g(k) be the gauge group of P-4,P-k classified by k epsilon', where epsilon' a generator of pi(8) (B(SU (4))) congruent to Z. In this article we partially classify the homotopy types of g(k) by showing that if there is a homotopy equivalence G(k) similar or equal to G(k), then (420, k) = (420, k') and if (3360, k) is equal to (3360, k') then g(k) similar or equal to g(k'). (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：8

共 19 条

[1] 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

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

Crabb, MC ;

Sutherland, WA .

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

[3] The homotopy types of Sp(3)-gauge groups [J].

Cutler, Tyrone .

TOPOLOGY AND ITS APPLICATIONS, 2018, 236 :44-58

[4] 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

[5] On [X, U(n)] when dim X is 2n [J].

Hamanaka, H ;

Kono, A .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2003, 43 (02) :333-348

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

Hamanaka, Hiroaki ;

Kaji, Shizuo ;

Kono, Akira .

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

[7] Homotopy type of gauge groups of SU(3)-bundles over S6 [J].

Hamanaka, Hiroaki ;

Kono, Akira .

TOPOLOGY AND ITS APPLICATIONS, 2007, 154 (07) :1377-1380

[8] On the cellular decomposition and the Lusternik-Schnirelmann category of Spin(7) [J].

Iwase, N ;

Mimura, M ;

Nishimoto, T .

TOPOLOGY AND ITS APPLICATIONS, 2003, 133 (01) :1-14

[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]

Kishimoto D., ARXIV180306477V2

← 1 2 →