The homotopy types of Sp(n)-gauge groups over S^4m

2022/04/19 by Mohammadi, Sajjad
#Algebraic Topology (math.AT) #FOS: Mathematics #Primary $54C35$ #Secondary $55P15$

paper · doi:10.48550/arxiv.2204.08867

Abstract

Let m and n be two positive integers such that m < n. Denote by P_n,k the principal Sp(n)-bundle over S^4m and G_k,m(Sp(n)) be the gauge group of P_n,k classified by kε', where ε' is a generator of π_4m(B(Sp(n)))≅ℤ. In this article, we will partially classify the homotopy types of G_k,m(Sp(n)) by giving a lower bound for the number of homotopy types of G_k,m(Sp(n)). Also, in special cases Sp(3)-gauge groups over S⁸ and Sp(4)-gauge groups over S¹² we give an upper bound for the number of homotopy types of these gauge groups.

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