Abstract
AbstractWe define the discrete degree of symmetry disc-sym(X) of a closed n-manifold X as the biggest $$m\ge 0$$
m
≥
0
such that X supports an effective action of $$(\mathbb {Z}/r)^m$$
(
Z
/
r
)
m
for arbitrarily big values of r. We prove that if X is connected then disc-sym$$(X)\le 3n/2$$
(
X
)
≤
3
n
/
2
. We propose the question of whether for every closed connected n-manifold X the inequality disc-sym$$(X)\le n$$
(
X
)
≤
n
holds true, and whether the only closed connected n-manifold X for which disc-sym(X)$$=n$$
=
n
is the torus $$T^n$$
T
n
. We prove partial results providing evidence for an affirmative answer to this question.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
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