
Journal of Lie Theory 32 (2022), No. 3, 697708 Copyright Heldermann Verlag 2022 A CharacteristicIndex Inequality for Closed Embeddings of Locally Compact Groups Alexandru Chirvasitu Dept. of Mathematics, University at Buffalo, New York, U.S.A. achirvas@buffalo.edu [Abstractpdf] The characteristic index of a locally compact connected group $G$ is the nonnegative integer $d$ for which we have a homeomorphism $G\cong K\times \mathbb{R}^d$ with $K$ maximal compact in $G$. We prove that the characteristic indices of closed connected subgroups are dominated by those of the ambient groups. Keywords: Lie group, locally compact group, characteristic index, dense embedding, Lie algebra, homology, fibration, spectral sequence. MSC: 22D05, 22E15, 22E60, 57T15, 55T10. [ Fulltextpdf (115 KB)] for subscribers only. 