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Results tagged with gt.geometric-topology
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user 4625
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).
25
votes
Accepted
What would the slice-ribbon conjecture imply?
I think of the ribbon-slice conjecture as a wish that would simplify certain 4D questions. Let me explain this in 3 examples.
Given an embedded "ribbon disk" in 4-space (where the Morse function has …
- 1,696
21
votes
Failure of smoothing theory for topological 4-manifolds
John, if you look at chapter 8 of Freedman-Quinn's book on topological 4-manifolds, you'll find the following computation of the homotopy groups of Top(4)/O(4):
$\pi_3 = Z/2$ and $\pi_i = 0$ for $i=0 …
- 1,696
13
votes
Accepted
Natural examples of finite dimensional spaces with interesting 2-type
The 2-type of a 4-manifold is an extremely interesting invariant. In fact, work of Hambleton and Kreck shows that in many cases it determines the homotopy type (if one adds the intersection form as an …
- 1,696
12
votes
Accepted
slice-ribbon for links (surely it's wrong)
Ryan, I think this is an open problem. The best related result I know is a theorem of Casson and Gordon [A loop theorem for duality spaces and fibred ribbon knots. Invent. Math. 74 (1983)] saying that …
- 1,696
10
votes
Accepted
A problem/conjecture related to 4-manifolds that deserves a name. What name does it deserve?
I think that the conjecture is wrong. The following leads to counterexamples in the topological category and probably also smoothly: Take a closed oriented 4-manifold N with infinite cyclic fundamenta …
- 1,696