Homotopy types of gauge groups over non-simply-connected closed 4-manifolds

2016/09/08 by Tse Leung So, So, Tse Leung
Mathematics · #55P40 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 54C35 #Secondary 55R10 #math.AT #msc:54C35 #msc:55P40 #msc:55R10

paper · pdf · doi:10.48550/arxiv.1609.02486

21 pages; accepted by Glasgow Mathematical Journal

arxiv created 2018/06/11 · arxiv updated 2018/06/12

Abstract

Let G be a simply-connected simple compact Lie group and let M be an orientable smooth 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/p^rℤ, or (3)~ℤ^*m*(*ⁿ_j=1ℤ/p_j^r_jℤ), where p and the p_j's are odd primes.

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