# Talk:Fundamental domain

## Suggestions

This page should probably be merged with free regular set.linas 17:17, 15 Feb 2005 (UTC)

Nahh. linas 05:19, 9 November 2006 (UTC)

## Knots

Some of the hyperbolic ones are related to knot complements. e.g. the classic number theory one is the complement of the trefoil knot mod the stabilizer SO(2). Or something like that. Note the presentation y^2=x^3 for the trefoil is the same presentation as for the modular group. Or something like that. Or so I overheard at a party. What I'd like to know is ... are all homogeneous spaces knot complements? if not, why not? linas 05:19, 9 November 2006 (UTC)

## General definition ?

Hello, I am wondering if the definition given in the article is general enough (a fundamental domain is a set D of representatives for the cosets of Γ in G, Γ being a lattice of the Lie group G). The article on Mathworld doesn't make any reference to Lie groups. I must also say that as a newcomer to these theories, I find the definition from Mathworld clearer. Is it legal to just copy it? (just the definition, which should be public domain). --Mathieu Perrin (talk) 06:07, 2 March 2008 (UTC)

## modular group

"The standard fundamental domain of the modular group probably deserves a page of its own. Katzmik (talk) 14:11, 22 September 2008 (UTC)

## definition from MathWorld--Correct?

Let be a group and be a topological G-set. Then a closed subset of is called a fundamental domain of in if is the union of conjugates of , i.e., and the intersection of any two conjugates has no interior. For example, a fundamental domain of the group of rotations by multiples of in is the upper half-plane and a fundamental domain of rotations by multiples of is the first quadrant . The concept of a fundamental domain is a generalization of a minimal group block, since while the intersection of fundamental domains has empty interior, the intersection of minimal blocks is the empty set."

• I hope this is right, since the last sentence is due to me. I would say if it is right , that would be nice, because it is concise and seems easy to understand and use. The current wikipedia article, like many wikipedia math articles (such as how affine space USED to be)go on and on without giving an immediate, precise definition. Maybe that's necessary in the nature of these things and the clear, concise definition on MathWorld is wrong? I am genuinely concerned that I have contributed a plausible, userfriendly but wrong explanation to MathWorld.Rich (talk) 03:05, 10 February 2010 (UTC)