On Macbeath‘s formula for hyperbolic manifolds
Grzegorz Gromadzki , Rubén A. Hidalgo
AbstractAround 1973, Macbeath provided a formula for the number offixed points of an element in a groupGof conformal automorphisms of a closedRiemann surfaceSof genus at least two. Such a formula was initially used toobtain the character of the representation associated to the induced action ofGon the first homology group ofS, and later turned out to be extremely usefulin many other contexts. By using a simple counting procedure, we provide asimilar formula for the number of connected components of an element in afinite group of isometries of a hyperbolic manifold.
|Journal series||Albanian Journal of Mathematics, ISSN , e-ISSN 1930-1235, (0 pkt)|
|Publication size in sheets||0.5|
|Keywords in English||hyperbolic manifolds, fixed points, automorphisms|
|Score||= 5.0, 24-07-2019, ArticleFromJournal|
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