Seminarium z Topologii Algebraicznej
Wtorki, 12:15-13:45, sala 4070
Separability of embedded surfaces in 3-manifolds
Piotr Przytycki
20.11.2012
This is joint work with Dani Wise. Let S be an immersed
incompressible surface in a 3-manifold M. Denote by M' the universal cover
of M. Scott proved that the group pi_1S is separable in pi_1M iff any
compact neighborhood of S in pi_1S\M' embeds in some finite cover of M.
Rubinstein and Wang found an immersed surface which does not lift to an
embedding in a finite cover, hence violates this condition. We prove
that this is the only obstruction, i.e. that if S is already embedded, then
pi_1S is separable.