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Results tagged with gt.geometric-topology
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user 140203
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
5
votes
0
answers
243
views
The bridge index and crookedness of a knot
I am reading Dale Rolfsen's book KNOTS AND LINKS, at page 115, I can't figure out why the crookedness of a knot equals its bridge index. Please give me some hints or any references available, much tha …
- 502
3
votes
1
answer
338
views
Volume of hyperbolic 3-manifolds with toroidal boundary
A hyperbolic 3-manifold has finite volume if and only if it is either closed or has toroidal boundary and it is not homeomorphic to $T^2\times I$.
This statement is from 3-Manifold Groups, page 18 (th …
- 502
12
votes
Accepted
Irreducible 3-manifold with boundary of genus greater than 1
M is always aspherical, and hence a Eilenberg-Maclane space.
This is because $\pi_1(\partial M)$ embeds to $\pi_1(M)$, by the incompressibility condition. If the genus of the boundary is no less than …
- 502
3
votes
1
answer
191
views
Guts of 3-manifolds for sutured manifolds and pared manifolds
I found the notion "guts of three-manifolds" unclear to me. There exists "sutured guts" and "pared guts" in the literature, the well definedness of both are vague to me.
Sutured guts: The following de …
- 502