Department of Mathematics

Indian Institute Of Technology Madras , Chennai
  • Mathematics Department Shifted to NAC Office of the Department of Mathematics is moved from HSB to New Academic Complex (NAC) 5th and 6th Floor

Embedding of metric graphs on hyperbolic surfaces

Speaker : Bidyut Sanki, Institute of Mathematical Sciences, Chennai

30-07-2018

Abstract :

An embedding of a metric graph $(G, d)$ on a closed hyperbolic surface is called essential, if each complementary region has a negative Euler characteristic. We show, by construction, given any metric graph, its metric can be re-scaled so that it can be essentially and isometrically embedded on a closed hyperbolic surface. The essential genus $g_e(G)$ of a metric graph $(G, d)$ is the lowest genus of a surface on which such an embedding of the graph is possible. In the next result, we establish a formula to compute $g_e(G)$. Furthermore, we show that for every integer $g\geq g_e(G)$, $(G, d)$ can be essentially and isometrically embedded (possibly after a re-scaling the metric $d$) on a surface of genus $g$.

Key Speaker Bidyut Sanki, Institute of Mathematical Sciences, Chennai
Place Madhava Hall
Start Time 11:00 AM
Finish Time 12:01 PM
External Link None