Topology Seminar (Introductory Talk): Dirichlet domain and its volume

Seminar | January 23 | 2-3 p.m. | 740 Evans Hall

 Maria Trnkova, UC Davis

 Department of Mathematics

This will be an introductory talk to Dirichlet domain and volume computations in \(H^3\). We'll give a definition of a Dirichlet domain and discuss its tiling properties. Then we explore volume computation in a hyperbolic case. We review few special cases: orthoscheme, ideal tetrahedron and a tetrahedron with one ideal vertex. Then we generalize these computations for volume of any polyhedron in Hyperbolic Space. No background in Hyperbolic Geometry is required.