Statement
Given an oriented surface, we can divide group Diff(S) the diffeomorphisms of the surface to itself in isotopy classes to get the mapping class group π0(Diff(S)). The conjecture asks whether a finite group of the mapping class group of a surface can be realized as the isometry group of a hyperbolic metric on the surface.
The mapping class group acts on Teichmüller space. An equivalent way of stating the question asks whether every finite subgroup of the mapping class group fixes some point of Teichmüller space.
Read more about this topic: Nielsen Realization Problem
Famous quotes containing the word statement:
“A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.”
—J.L. (John Langshaw)
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)
“Truth is used to vitalize a statement rather than devitalize it. Truth implies more than a simple statement of fact. “I don’t have any whisky,” may be a fact but it is not a truth.”
—William Burroughs (b. 1914)