25,656 reputation
166150
bio website rybu.org
location Victoria, BC
age 41
visits member for 5 years, 5 months
seen 2 hours ago
I'm a professor of mathematics at the University of Victoria, in BC Canada.

3h
comment Studying topology: which first, algebraic or differential?
To answer the question, there's no reason to start with either. Why not just learn both at the same time?
3h
comment Studying topology: which first, algebraic or differential?
@FanZheng: this is a fairly different question. It's asking for a value judgement on learning a topic in a particular order. Generally speaking these kinds of "study advice" questions aren't treated particularly kindly here on MO. If asked in a fairly refined way, they do get tolerated, though.
10h
reviewed Close Invariance of absolute determinant under alternating sign changes in columns
22h
comment Descriptive Complexity of Knot Equivalence
Closely related thread: mathoverflow.net/questions/35680/complete-knot-invariant/…
Apr
16
reviewed Close Does hyperconnected imply path-connected
Apr
16
reviewed Close Is there a stochastic process with zero mean but nonzero value in each time instant?
Apr
16
reviewed Close Old Peano theorem (demonstration is missing details)
Apr
16
awarded  Popular Question
Apr
10
comment Hopf link from analytic geometry
@DelDon: perhaps you meant to ask a slightly different question? Linking numbers is a very coarse way of looking at things -- it fails to distinguish most links. If would be like being a condensed matter physicist and the only physical quantity you understood was viscosity. It gets you somewhere, but not very far, at least, not without a lot of work.
Apr
8
comment Show that the symplectic action 1-form on loop space is closed
Have you looked at various proofs of the Poincare Lemma? Typically it involves taking the derivative of an integral of the contraction of a form. This is precisely what you are interested in.
Apr
7
awarded  Necromancer
Apr
3
comment Finding commuting matrices
Your question is a little vague. As Noah mentions, at a not too high-level the answer is the solution of the linear system $AH=HA$, $BH=HB$. You could also answer the question at the level of canonical forms. More generally, two matrices commute if and only if they can be expressed as polynomials in some common matrix. I'm not sure if any of these are very useful to you. But you have not given us enough information to know what kind of answer you want.
Apr
2
reviewed Close Is a sigma-finite Borel measure over $\mathbb R$ determined by its values on the continuous functions?
Apr
2
reviewed Close Recursion and splitting into even and odd parts
Apr
2
comment What non-categorical applications are there of homotopical algebra?
Also, the higher homotopy groups of $Emb(S^1,S^3)$, with the exception of the unknot component, are the same as the higher homotopy groups of $S^3$. I don't think the embedding calculus offers much insights into that -- from this perspective the homotopy groups of spheres are building blocks rather than things to gain insight into.
Apr
2
comment What non-categorical applications are there of homotopical algebra?
It's quite unclear what the Goodwillie calculus sees of the homotopy-groups of $Emb(S^1,S^3)$. In contrast, it would appear to see "quite a bit" of the homology. But in homotopy, it looks like the calculus sees relatively little. For example, it would be very difficult to extract much of the non-abelian nature of $\pi_1 Emb(S^1,S^3)$ using the calculus. In higher dimensions $Emb(S^1,S^n)$ for $n > 3$ all those troubles vanish, though.
Apr
2
comment Ehresmann fibration theorem for manifolds with boundary
Take whichever proof you've seen in the manifold without boundary case and adapt it. I think the cleanest proof would be to apply the tubular neighbourhood theorem to the fibres. The fact that the map is a submersion allows you to trivialize the tubular neighbourhoods of the fibres (this also gives you the fibre bundle structure).
Apr
2
comment Ehresmann fibration theorem for manifolds with boundary
Yes a version of it is true if both $M$ and $N$ have boundary. The extra assumption you need is that when you restrict $f$ to the boundary of $M$ it maps that to the boundary of $N$, and that the restriction map $f_{|\partial M} : \partial M \to \partial N$ is a submersion. From these hypothesis, the proof is basically identical to the classical proof.
Mar
31
comment Generalize Gauss-Bonnet Formula to non-simple closed curves
You aren't really talking about an extension of the Gauss-Bonnet Formula, more just one of the standard ways of stating it. Isn't it stated essentially the above way in Milman-Parker, for instance?
Mar
31
reviewed Close A $C^{*}$ algebra associated to a group