The tag has no wiki summary.

learn more… | top users | synonyms

12
votes
1answer
230 views

Geometric intersection with incompressible surfaces

Let $M$ be a oriented compact $3$-manifold, closed or with boundary. For any incompressible surface $F$, define a function $i_F$ on the set of homotopy classes of closed curves in $M$ by $$i_F ...
7
votes
2answers
316 views

Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?

Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ where $\Sigma$ is any closed surface? I know of the Hatcher-Thurston classification of incompressible surfaces in 2-bridge ...
13
votes
1answer
307 views

compressibility of Seifert surface after 0-surgery

Gabai's solution of the Property R conjecture shows that a minimal genus Seifert surface of a knot, capped off in the 0-framed surgery along that knot, is of minimal genus in its homology class. In ...
2
votes
1answer
169 views

Example of hyperbolic 3-fold with no embedded incompressible subsurfaces

Kahn-Markovic show that every hyperbolic 3-fold contains an immersed $\pi_1$ injective surface. Are there any known examples of hyperbolic 3-folds that do not contain a embedded $\pi_1$ injective ...
8
votes
1answer
1k views

Incompressible surfaces in an open subset of R^3

Let $U$ be a connected open subset of $\mathbb R^3$. Furthermore, we have: $\mathbb R^3\setminus U$ has exactly two connected components (thus by Alexander duality, $H_2(U;\mathbb Z)=\mathbb Z$). ...