3,746 research outputs found
The geodesic flow on nilmanifolds associated to graphs
In this work we study the geodesic flow on nilmanifolds associated to graphs.
We are interested in the construction of first integrals to show complete
integrability on some compact quotients. Also examples of integrable geodesic
flows and of non-integrable ones are shown.Comment: 22 page
On the connectivity of proper power graphs of finite groups
We study the connectivity of proper power graphs of some family of finite
groups including nilpotent groups, groups with a non-trivial partition, and
symmetric and alternating groups.Comment: 13 page
Coxeter group actions on the complement of hyperplanes and special involutions
We consider both standard and twisted action of a (real) Coxeter group G on
the complement M_G to the complexified reflection hyperplanes by combining the
reflections with complex conjugation. We introduce a natural geometric class of
special involutions in G and give explicit formulae which describe both actions
on the total cohomology H(M_G,C) in terms of these involutions. As a corollary
we prove that the corresponding twisted representation is regular only for the
symmetric group S_n, the Weyl groups of type D_{2m+1}, E_6 and dihedral groups
I_2 (2k+1) and that the standard action has no anti-invariants. We discuss also
the relations with the cohomology of generalised braid groups.Comment: 11 page
Specular sets
We introduce the notion of specular sets which are subsets of groups called
here specular and which form a natural generalization of free groups. These
sets are an abstract generalization of the natural codings of linear
involutions. We prove several results concerning the subgroups generated by
return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352
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