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Jan
26
comment Uniform continuity of length function on geodesic currents
The currents space $C(S)$ has a natural metrizable uniform structure, defined by Bonahon at the bottom of page 141 of his paper.
Nov
23
comment Complements of unknotted tori (higher dimensions)
what is the definition of an unknotted torus in $S^{n+1}$?
Oct
23
comment What makes four dimensions special?
yes, you're right, I have added this hypothesis, thanks
Oct
23
revised What makes four dimensions special?
added 30 characters in body
Aug
21
comment Gluing two diffeomorphisms and then smoothing
Yes, it can, because you can pick two collars of the boundaries, and isotope each diffeomorphism $\phi^\pm$ so that it acts productwise on each collar. This is also the same technique one uses to prove that two smooth isotopies can be composed and transformed into a smooth isotopy.
May
20
awarded  Yearling
Apr
13
awarded  Nice Question
Apr
7
awarded  Popular Question
Feb
5
awarded  Good Answer
Jan
23
comment Fox re-imbedding theorem in dimension four
More generally, which re-imbedding techniques do we know? If I have a 3-manifold in S^4, how can I modify its embedding so that it is not isotopic to the previous one?
Dec
9
revised Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
added 3 characters in body
Dec
9
revised Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
fix
Dec
9
answered Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
Dec
3
comment Can knot diagrams be monotonically simplified using under moves?
As suggested by Marco, this knot can be fully simplified via level moves, see zanellati.it/knot/Satellite_knot.pdf I just got this information from the author of the program who is following this page, so drawings of more complicated unknots are welcome :-) It would be interesting to try one more additional doubling as suggested by Joel...
Nov
28
awarded  Nice Answer
Nov
24
answered Additivity of simplicial volume
Nov
4
comment Examples of Einstein four-manifolds of negative sectional curvature
using Dehn filling on cusped hyperbolic manifolds (see the papers of Anderson and Bamler) you can construct plenty of manifolds that admit both Einstein and non-positive sectional curvature metrics, but not simultaneously as far as I understand.
Nov
4
comment Can knot diagrams be monotonically simplified using under moves?
I don't know (I still haven't seen the program running), but if you perform the diagram connected sum I suppose it simplifies the knot exactly as before. One should try some hard version of the trefoil knot...
Nov
4
revised Can knot diagrams be monotonically simplified using under moves?
picture
Nov
4
answered Can knot diagrams be monotonically simplified using under moves?