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Results tagged with gt.geometric-topology
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user 1587
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).
8
votes
Why are there no wild arcs in the plane?
By stereographic projection we can assume that the given Jordan arc
lies on a sphere, and that its two ends are at opposite poles, $N$
and $S$. Now project the arc onto a cylinder that touches the sph …
- 12.4k
25
votes
Accepted
Turning pants inside-out (or backwards) while tied together
I think that the answer is no, by consideration of linking numbers.
First simplify the human body plus cord joining the ankles to a circle, and
assign it an orientation. Also assign an orientation to …
- 12.4k
7
votes
Who first used the cross-ratio to describe shapes in hyperbolic geometry?
I've hesitated to attempt an answer to this question because
I do not know about shape parameters. However, in the hope that
what is really wanted is a history of the cross-ratio, here goes.
The cro …
- 12.4k
8
votes
solvable word problem without algorithm
The technique for constructing groups with unsolvable word problems
applies more generally to construct groups that "simulate'' Turing
machines. So, if a Turing machine halts for a recursive set of in …
- 12.4k
28
votes
Applications of infinite graph theory
The first book on graph theory was König's Theorie der endlichen und
unendlichen Graphen (Theory of finite and infinite graphs) of 1936.
Thus infinite graphs were part of graph theory from the very be …
- 12.4k
44
votes
Fundamental groups of noncompact surfaces
I'm reluctant to advertise, but since no one else has answered yet,
I'll mention the proof on pp. 142--144 of my book Classical Topology
and Combinatorial Group Theory.
- 12.4k