Geometry, Topology and Dynamics Seminar
Loretta Bartolini
Loyola University Chicago
Incompressible one-sided surfaces and Dehn filling
Abstract: Two-sided surfaces are widely used in 3-manifold theory, particularly
when incompressible or giving a Heegaard splitting. However, methods are often
limited by insufficient control over such surfaces, or difficulties in their
identification.
One-sided surfaces likewise offer a geometric insight into a 3-manifold,
however, the direct correspondence between such surfaces and $\mathbb{Z}_2$ homology
offers a structure within which the surfaces may be controlled. This allows
manipulation and classification of one-sided surfaces where two-sided surfaces
are not easily studied, in particular, under Dehn filling. A classification of
geometrically incompressible one-sided surfaces in an infinite class of closed
hyperbolic 3-manifolds is given. Looking ahead, the connection between $\mathbb{Z}_p$
homology and hyperbolic structures provides interesting avenues for future
study.
Monday November 28, 2011 at 3:00 PM in SEO 636