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Results tagged with gt.geometric-topology
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user 10909
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).
12
votes
1
answer
596
views
Pseudogroups and the flavors of the topology of manifolds
Topologists study topological manifolds, differentiable manifolds and PL-manifolds (and some other flavors), with each class distinguished by the selection of a pseudogroup that restricts the transiti …
- 17.6k
23
votes
Accepted
Mazur's unpublished manuscript on primes and knots?
This showed up in my snail-mail today, so I'm sharing the wealth:
http://ifile.it/rodc5is/mazur.pdf
- 17.6k
36
votes
3
answers
5k
views
Mazur's unpublished manuscript on primes and knots?
The story of the analogy between knots and primes, which now has a literature, started with an unpublished note by Barry Mazur.
I'm not absolutely sure this is the one I mean, but in his paper, Analo …
- 17.6k
9
votes
2
answers
986
views
Manifolds with rectifiable curves
To begin with, observe that the notion of a rectifiable curve makes sense in, say, a smooth or a PL-manifold but not in merely a topological manifold. Indeed if $f:[0,1]\rightarrow U\subset{\Bbb R}^n …
- 17.6k
5
votes
0
answers
280
views
A certain kind of proof of the Hairy Ball Theorem
I'd just like to know if proofs of the Hairy Ball Theorem along the following lines are well-known or even somewhere in the literature.
From a given vector field $V_1$ on $S^2$, form another, $V_2$, b …
- 17.6k
11
votes
4
answers
1k
views
Knot diagrams, sets of moves and equivalence relations
Short version: Does anyone study equivalence classes generated by a given set of "moves" (in the sense of, but not limited to, Reidemeister moves) on the set of knot diagrams?
Yes, I understand that …
- 17.6k