Ryan Budney
Reputation
408/400 score
 5h comment Contradiction about the existence of God This is way off topic for the forum. 18h accepted Looking for “large knot” examples 18h comment Looking for “large knot” examples Sam, the problem is my own example was an answer to my question and I had not realized it. I'll accept Allison's, although it was Neil's answer that made me realize what was going on. 1d comment Number of critical points of a smooth function What's the "stable morse number" of a manifold? When I google it I only get the paper mentioned by Chris Gerig, and it's behind a paywall. May 3 comment Relation between Harmonic vector field and Harmonic 1-form Harmonic forms are almost never unit length, as far as I am aware. It would appear to me that Definition 1 is a very special definition, largely unrelated to Definition 2. You can of course talk about harmonic vector fields (i.e. dual to harmonic forms) but this results in a different object than your "harmonic unit vector fields". May 3 answered Poincare-Hopf theorem for polytopes? Apr 22 comment Free operads and trees I prefer to think of free objects in terms of the universal property they satisfy. You do whatever constructions you have to do to satisfy that universal property. If it involves trees, so be it. With symmetric operads, trees are not precisely the structures you need -- you label the vertices of the trees and mod out by an equivalence relation. This is no longer a tree structure. Apr 21 comment Measure of the Attractor of Critical Points of a Manifold You are free to make assumptions through a fairly wide universe of possible assumptions that would lead to consequences. For example, if you had a bound on the 4-th derivative of $f$ you could convert that into a lipschitz bound on the derivative of the gradient. . . which would give you a lower bound on the diameter of a ball contained in the stable manifold of a critical point. In which ever context you are in, does the fourth derivative of $f$ come up? Apr 20 awarded Revival Apr 20 reviewed Close PDE with harmonic function Apr 20 reviewed Close Understanding Strong Normalization for Identity Types in Martin-Löf Intensional Type Theory Apr 20 reviewed Close Reflexive sheaf and torsion free sheaf Apr 20 reviewed Close Canonical module of a Buchsbaum ring Apr 20 reviewed Close A subset of a Grassmanian Apr 20 comment Triangulation of S^2xS^2 I believe the minimal triangulation of $S^2 \times S^2$ has 6 $4$-dimensional simplices. It depends on what your "rules" for triangulations are. I'm using unordered delta complexes. Do you want a simplicial triangulation? You'll need many more simplices in that case. Apr 20 answered Homotopy type of diffeomorphism which are the identity on and near the boundary Apr 20 answered Constructing a “nice” cobordism Apr 17 comment About stable manifold of a point What would distinguish an answer from simply restating the condition in your question? I suppose I don't see a non-trivial aspect to your question. Apr 15 comment Do Morse functions induce embeddings? No, there's little relation between Morse functions and embeddings. Given an embedding in euclidean space you can make the projections to the coordinate axis Morse functions. . . and similarly given an embedding in a suitably high-dimensional space you can ensure any morse function can be realized as a coordinate function. Those are the only close relations that come to mind. Apr 14 reviewed Close How do I ensure that my matrix is positive definite?