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Results tagged with gt.geometric-topology
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user 9248
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).
18
votes
Accepted
Why are $S^3-K$ and $\operatorname{SL}(2,\mathbb R)/{\operatorname{SL}(2, \mathbb Z)}$ diffe...
Here is a sketch:
$\DeclareMathOperator\SL{SL}\SL(2,\mathbb R)/{\SL(2,\mathbb Z)}$ can be identified with the space of lattices of covolume 1 in $\mathbb R^2$. Indeed, $\SL(2, \mathbb R)$ can be ident …
- 1,875
5
votes
1
answer
158
views
Exchanging the components of a two-component link
Given a 2-component link in $S^3$ whose components are trivial knots, is it always possible to find a homeomorphism of $S^3$ that exchanges the components?
I guess the answer is "no" (but I could not …
- 1,875
12
votes
2
answers
1k
views
Genus one fibered links
It is well-known that the only genus one fibered knots are the trefoil and the figure-eight. On the other hand, there exist infinitely many fibered links for any fixed higher genus.
My question is ab …
- 1,875
12
votes
3
answers
1k
views
Fibered knot with periodic homological monodromy
It is well-known that there exist pseudo-Anosov automorphisms of surfaces that act trivially on the homology: they form the Torelli group. Similarly there exists pseudo-Anosov automorphisms that act p …
- 1,875
40
votes
Accepted
Tying knots with reflecting lightrays
These knots seem to be called billiard knots in the literature. They coincide with Lissajous knots as shown by Jones and Przytycki in "Lissajous knots and billiard knots", Banach center Publications 4 …
- 1,875