Finding disjoint surfaces in 3-manifolds

Author: 

Lackenby, M

Publication Date: 

1 January 2014

Journal: 

Geometriae Dedicata

Last Updated: 

2019-04-27T21:17:47.817+01:00

Issue: 

1

Volume: 

170

DOI: 

10.1007/s10711-013-9886-6

page: 

385-401

abstract: 

Let M be a compact connected orientable 3-manifold, with non-empty boundary that contains no two-spheres. We investigate the existence of two properly embedded disjoint surfaces S1 and S2 such that M - (S1 ∪ S2) is connected. We show that there exist two such surfaces if and only if M is neither a Z2 homology solid torus nor a ℤ2 homology cobordism between two tori. In particular, the exterior of a link with at least three components always contains two such surfaces. The proof mainly uses techniques from the theory of groups, both discrete and profinite. © 2013 Springer Science+Business Media Dordrecht.

Symplectic id: 

466888

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article