scholarly journals The Homotopy Types of Sp(2)-Gauge Groups over Closed Simply Connected Four-Manifolds

2019 ◽  
Vol 305 (1) ◽  
pp. 287-304
Author(s):  
Tseleung So ◽  
Stephen Theriault
Keyword(s):  
Gauge Groups ◽  
Homotopy Types ◽  
Four Manifolds ◽  
Simply Connected

scholarly journals HOMOTOPY TYPES OF GAUGE GROUPS OVER NON-SIMPLYCONNECTED CLOSED 4-MANIFOLDS

2018 ◽  
Vol 61 (2) ◽  
pp. 349-371 ◽  
Author(s):  
TSELEUNG SO
Keyword(s):  
Homotopy Type ◽  
Lie Group ◽  
Compact Lie Group ◽  
Gauge Groups ◽  
Homotopy Types ◽  
Simply Connected

AbstractLet G be a simple, simply connected, compact Lie group, and let M be an orientable, smooth, connected, closed 4-manifold. In this paper, we calculate the homotopy type of the suspension of M and the homotopy types of the gauge groups of principal G-bundles over M when π1(M) is (1) ℤ*m, (2) ℤ/prℤ, or (3) ℤ*m*(*nj=1ℤ/prjjℤ), where p and the pj's are odd primes.

scholarly journals Odd primary homotopy types of SU(n)–gauge groups

2017 ◽  
Vol 17 (2) ◽  
pp. 1131-1150 ◽  
Author(s):  
Stephen Theriault
Keyword(s):  
Gauge Groups ◽  
Homotopy Types

scholarly journals Einstein Four-Manifolds With Self-Dual Weyl Curvature of Nonnegative Determinant

2019 ◽  
Author(s):  
Peng Wu
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
The Self ◽  
Weyl Curvature ◽  
Positive Scalar ◽  
Four Manifolds ◽  
Simply Connected

Abstract We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally Kähler if and only if the determinant of the self-dual Weyl curvature is positive.

ON POSITIVELY CURVED FOUR-MANIFOLDS WITH S1-SYMMETRY

2011 ◽  
Vol 22 (07) ◽  
pp. 981-990 ◽  
Author(s):  
JIN HONG KIM
Keyword(s):  
Topological Classification ◽  
Circle Action ◽  
Torus Action ◽  
Dimensional Manifold ◽  
Linear Action ◽  
Circle Actions ◽  
Four Manifolds ◽  
Simply Connected ◽  
Diffeomorphism Classification ◽  
Positively Curved

It is well known by the work of Hsiang and Kleiner that every closed oriented positively curved four-dimensional manifold with an effective isometric S1-action is homeomorphic to S4 or CP2. As stated, it is a topological classification. The primary goal of this paper is to show that it is indeed a diffeomorphism classification for such four-dimensional manifolds. The proof of this diffeomorphism classification also shows an even stronger statement that every positively curved simply connected four-manifold with an isometric circle action admits another smooth circle action which extends to a two-dimensional torus action and is equivariantly diffeomorphic to a linear action on S4 or CP2. The main strategy is to analyze all possible topological configurations of effective circle actions on simply connected four-manifolds by using the so-called replacement trick of Pao.

On p-local homotopy types of gauge groups

2014 ◽  
Vol 144 (1) ◽  
pp. 149-160 ◽  
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono ◽  
Mitsunobu Tsutaya
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Principal Bundle ◽  
Dimensional Sphere ◽  
Gauge Groups ◽  
Homotopy Types

The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

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