Clay–Mahler specialist lecture, Univ. Melbourne
Name: | Clay–Mahler specialist lecture, Univ. Melbourne |
Calendar: | 1-day meetings & lectures |
When: | Fri, July 24, 2009, 12:15 am - 2:15 am |
Description: |
Abstract: Surface subgroups from homologyThis is the first lecture in a series on scl (stable commutator length). scl answers the question: what is the simplest surface in a given space with prescribed boundary?, where simplest is interpreted in topological terms. This topological definition is complemented by several equivalent definitions:
On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. On the linear programming side, scl is measured in terms of certain functions called quasimorphisms, which arise from hyperbolic geometry (negative curvature) and symplectic geometry (causal structures). We will discuss how scl in free and surface groups is connected to such diverse phenomena as the existence of closed surface subgroups in graphs of groups, rigidity and discreteness of symplectic representations, bounding immersed curves on a surface by immersed subsurfaces, and the theory of multi-dimensional continued fractions and Klein polyhedra. |
Location: | Richard Berry Building, University of Melbourne Map |
URL: | /tiki-read_article.php?articleId=61 |
Created: | 01 Aug 2009 07:13 pm UTC |
Modified: | 08 Aug 2009 05:17 am UTC |
By: | rmoore |
Status: | Confirmed |