15,119 reputation
32765
bio website rybu.org
location Victoria, Canada
age 40
visits member for 3 years, 8 months
seen 7 hours ago

I am a professor of mathematics at the University of Victoria, in Canada.


8h
reviewed Close Topological graph theory question
8h
reviewed Close Integrate the function $x^x$?
8h
reviewed Close Prove something is divisible by a prime
8h
reviewed Close Probability math problem.
8h
reviewed Close How prove $|S-10^k\cdot AB|\le 9k$
18h
comment Given a diffeomorphism between two surfaces, is there an expression for the pullback of the covariant derivative of a vector field?
In what way are your metrics "linked"?
1d
comment Given a diffeomorphism between two surfaces, is there an expression for the pullback of the covariant derivative of a vector field?
You could express it as $\nabla^{f^*B} F^* X^B$, i.e. the covariant derivative with respect to the pulled-back connection.
1d
comment Measuring distance on the Poincare disk
This comes from the Minkowski model of hyperbolic geometry, also called the Hyperboloid model. You are viewing the hyperbolic plane as a `sphere' in a vector space with an indefinite full-rank quadratic form.
2d
comment Where have I gone wrong in understanding of CW complex and Cell homology?
CW-complexes are defined inductively. First you define 0-dimensional CW-complexes as a disjoint union of points. Then 1-dimensional CW-complexes as 0-dimensional CW-complexes with 1-cells attached. Then 2-dimensional CW-complexes as 1-dimensional CW-complexes with 2-cells attached, etc. So an $n$-cell admits the structure of a CW-complex, but it actually admits many such structures.
Apr
19
comment Chain Rule to Compute Second Derivative
I give this as an exercise in my manifold theory course, too. The lecture notes are up on my webpage if you'd like to see the set-up. The key idea is to have two frameworks for the derivative. (1) Think of the derivative as a map of tangent bundles and (2) As a matrix that depends on points in $A$. Then express the 2nd derivative (tangent bundle formulation) in terms of the classical Hessian. From there the result pops out of two applications of the chain rule. $D^2(g \circ f) = D(Dg \circ Df) = D^2g \circ D^2f$.
Apr
16
comment lagrange multiplier---minimize
Why not show your work using the Lagrange multiplier method? It works fine for me.
Apr
16
answered Proving that the fundamental group of Klein bottle is generated by two elements without using covering spaces and van Kampen theorem, etc.
Apr
14
revised Topologist's Comb
edited tags
Apr
14
comment Topologist's Comb
So what have you done?
Apr
10
comment Notation question: What does $\langle X, - \rangle$ exactly mean?
Google "inner product"?
Apr
7
awarded  Nice Answer
Apr
4
revised No hypersurface with odd Euler characteristic
edited body
Apr
3
awarded  Nice Answer
Mar
24
awarded  Nice Answer
Mar
13
comment Do the composition of two Knots always yield a distinct knot (ignoring orientation)?
Regarding Q1, yes. Q2 also yes. Regarding your final (unnumbered) question, no. If $K_1$ and $K_2$ are both non-invertible, and if $\iota K_2$ denotes the inverse/reverse of $K_2$, then $K_1 \# K_2$ and $K_1 \# \iota K_2$ are not isotopic knots.