Triangle groups, automorphic forms, and torus knots

Details Triangle groups, automorphic forms, and torus knots Triangle groups, automorphic forms, and torus knots

2010-11-01

arxiv.org/abs/1011.0461v2

Mathematics

Geometric Topology

Corrections

Scientific paper

This paper deals with the relation between several classical and well-known objects: triangle Fuchsian groups, quasi-homogeneous singularities of plane curves, torus knot complements in the 3-sphere. Torus knots are the only nontrivial knots whose complements admit transitive Lie group actions. In fact S^3\K_{p,q} is diffeomorphic to a coset space of the universal covering group of PSL_2(R) with respect to a discrete subgroup G contained in the preimage of a (p,q,\infty)-triangle Fuchsian group. The existence of such a diffeomorphism between is known from a general topological classification of Seifert fibred 3-manifolds. Our goal is to construct an explicit diffeomorphism using automorphic forms. Such a construction is previously known for the trefoil knot K_{2,3} and in fact S^3\K_{2,3} = SL_2(R)/SL_2(Z). The connection between the two sides of the diffeomorphism comes via singularities of plane curves.

Affiliated with

Also associated with

No associations

Rating

Triangle groups, automorphic forms, and torus knots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Triangle groups, automorphic forms, and torus knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Triangle groups, automorphic forms, and torus knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594098