On the number of simplices required to triangulate a Lie group

Abstract

Abstract We estimate the number of simplices required for triangulations of compact Lie groups. As in the previous work [11] , our approach combines the estimation of the number of vertices by means of the covering type via a cohomological argument from [10] , and application of the recent versions of the Lower Bound Theorem of combinatorial topology. For the exceptional Lie groups, we present a complete calculation using the description of their cohomology rings given by the first and third authors. For the infinite series of classical Lie groups of growing dimension d, we estimate the growth rate of number of simplices of the highest dimension, which extends to the case of simplices of (fixed) codimension d − i .