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Estimate of number of simplices of triangulations of Lie groups

Research paper by Haibao Duan, Wacław Marzantowicz, Xuezhi Zhao

Indexed on: 31 Mar '20Published on: 29 Mar '20Published in: arXiv - Mathematics - Algebraic Topology



Abstract

We present estimates of number of simplices of given dimension of classical compact Lie groups. As in the previous work \cite{GMP2} the approach is a combination of an estimate of number of vertices with a use of valuation of the covering type by cohomological argument of \cite{GMP} and application of the recent versions of the Lower Bound Theorem of combinatorial topology. For the case of exceptional Lie groups we made a complete calculation using the description of their cohomology rings given by the first and third author. For infinite increasing series of Lie groups of growing dimension $d$ the rate of growth of number of simplices of highest dimension is given which extends onto the case of simplices of (fixed) codimension $d-i$.