23,340 reputation
151135
bio website rybu.org
location Victoria, BC
age 41
visits member for 4 years, 11 months
seen 4 hours ago
I'm a professor of mathematics at the University of Victoria, in BC Canada.

12h
comment A metric on $S^{2}$
Just use Cartesian coordinates together with the equivariance of the map. Alternatively, you could use one of the local models for the mas as a Seifert-fibred space, like how Hatcher describes the map in his 3-manifolds notes.
13h
comment A metric on $S^{2}$
I agree with Mariano, one can compute this metric directly. I've voted to close.
2d
comment Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
Is there any particular dictionary for surfaces you would like to use, Mohammad? The surface has fairly direct descriptions in most ways I can think of thinking of surfaces.
2d
comment Tangent space describes the manifold's first order characteristic. Is there something like tangent space describes higher order characteristic?
The derivative is on the tangent bundle $df : TM \to TN$, so the 2nd order derivative is a map of the tangent bundle of the tangent bundle, $d^2f : T^2M \to T^2N$. And so on.
Oct
16
reviewed Close Solution of parabolic PDE system
Oct
16
reviewed Close Analytic extension of the exterior Newtonian potential into the domain
Oct
16
reviewed Close Tracy-Widom distribution - Phase transitions - catastrophe/chaos - 'surface-fit'/'curve-fit' software
Oct
15
comment Slice a compact C1 surface in R3 by a moving transverse plane. Does the length of the slice depend C1 on the plane?
I think the difficult-looking appearance of your question has to do with your choice of coordinates. If instead of comparing the Riemann metric on your curves to the domain of $f$, i.e. $[0,1]$ you compare them directly, you get a much better sense for how the length varies. If your two curves are uniformly $C^1$-close, orthogonal projection from one to the other (using the normal line to the tangent space) gives a natural map between the two and allows you to compare their lengths with less bias. I think if you write out the details this answers your question.
Oct
15
comment Geodesics on a perturbed submanifold of $\mathbb{R}^m$
Start with Hirsch's Differential Topology text. It's covered quite well there.
Oct
15
comment Geodesics on a perturbed submanifold of $\mathbb{R}^m$
Usually one uses the tubular neighbourhood theorem to define a topology on a space of manifolds, like your situation. This turns it into a Frechet or Hilbert manifold depending on your precise setup. For (2), one uses the smooth dependence on initial conditions for the geodesic flow.
Oct
15
awarded  Nice Answer
Oct
14
comment Why the Dold-Thom theorem?
Give me a few days. My inbox has become thick in the past few...
Oct
14
comment Ehresmann's fibration theorem in the C1 class
Could you state a precise version of Ehresmann's theorem, for the sake of making your question concrete? Ehresmann's theorem, regardless of which version you use is basically just an application of the implicit function theorem. You can use the tubular neighbourhood theorem to speed up the proof and make it a little more conceptual. If you add in Riemann metrics and use the exponential map you can (very much!) speed up the proof but you bring in the $C^2$ assumption.
Oct
12
comment Homeo-Fixed point property
@VítTuček: where is the property regarding continuous functions mentioned?
Oct
12
comment Combinatorial spin structures
I've done a set of revisions to the paper, hopefully you find this one easier to read. An updated version of my paper will appear on the arXiv on Tuesday (October 14th, 2014). I went over the paper in detail last week and found some sign errors and some changes of conventions that happened without explanation. I'd love to hear about simplifications of this formalism, especially ones that work for arbitrary triangulations, but ones that work for special triangulations would interest me as well.
Oct
9
comment Homeo-Fixed point property
In your question you refer to two properties. But I only see one property defined. To me your question reads: is there an example of something with property X but does not satisfy property X.
Oct
8
comment Can knot diagrams be monotonically simplified using under moves?
I'd imagine you could ensure over/under moves are insufficient by doing something like a Whitehead doubling operation on your original knot. Or a cabling.
Oct
8
reviewed Close Largest eigenvalue of the sum of hermitian matricies
Oct
8
reviewed Close Finite Dimensionality of cohomology groups for normal varieties
Oct
7
comment Question about general torus knot lengths
What precisely do you mean by your major and minor radius? Parts of your question sound like a physical knot theory question, but other parts sound rather different. I suspect like Anthony that this may not be a knot theory question, perhaps more of a differential geometry question for a very specific embedding of the torus knot in $\mathbb R^3$.