Affiliation:
1. Faculty of Mathematics and Physics , University of Ljubljana , Jadranska 21, 1000 Ljubljana , Slovenia
2. Faculty of Mathematics and Computer Science , Adam Mickiewicz University of Poznań , ul. Uniwersytetu Poznańskiego 4, 61-614 Poznań , Poland
Abstract
Abstract
In a recent publication
[D. Govc, W. A. Marzantowicz and P. Pavešić,
Estimates of covering type and the number of vertices of minimal triangulations,
Discrete Comput. Geom. 63 2020, 1, 31–48],
we have introduced a new method, based on
the Lusternik–Schnirelmann category and the cohomology ring of a space X, that yields lower bounds
for the size of a triangulation of X. In this current paper, we present an important extension
that takes into account the fundamental group of X. In fact, if
π
1
(
X
)
{\pi_{1}(X)}
contains elements of
finite order, then one can often find cohomology classes of high ‘category weight’, which in turn
allow for much stronger estimates of the size of triangulations of X. We develop several weighted
estimates and then apply our method to compute explicit lower bounds for the size of triangulations of
orbit spaces
of cyclic group actions on a variety of spaces including products of spheres, Stiefel manifolds,
Lie groups and highly-connected manifolds.
Subject
Applied Mathematics,General Mathematics
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