A characteristic-index inequality for closed embeddings of locally compact groups

2021/07/31 by Chirvasitu, Alexandru
#22D05 #22E15 #22E60 #55T10 #57T15 #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2108.00341

Abstract

The characteristic index of a locally compact connected group G is the non-negative integer d for which we have a homeomorphism G≅ K× ℝ^d with K≤ G maximal compact. We prove that the characteristic indices of closed connected subgroups are dominated by those of the ambient groups.

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