On Macbeath‘s formula for hyperbolic manifolds

Grzegorz Gromadzki , Rubén A. Hidalgo

Abstract

Around 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.
Author Grzegorz Gromadzki (FMPI / IM)
Grzegorz Gromadzki,,
- Institute of Mathematics
, Rubén A. Hidalgo
Rubén A. Hidalgo,,
-
Journal seriesAlbanian Journal of Mathematics, ISSN , e-ISSN 1930-1235, (0 pkt)
Issue year2018
Vol12
No1
Pages15-23
Publication size in sheets0.5
Keywords in Englishhyperbolic manifolds, fixed points, automorphisms
URL http://albanian-j-math.com/archives/2018-03.pdf
Languageen angielski
Score (nominal)5
ScoreMinisterial score = 0.0, 21-03-2019, ArticleFromJournal
Ministerial score (2013-2016) = 5.0, 21-03-2019, ArticleFromJournal - czasopismo zagraniczne spoza list
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