1
vote
0answers
135 views
Definitions of definable compactness
We have an o-minimal structure M with the order topology. $X \subseteq M^n$ with the induced topology. The article "Definable compactness and definable subgroups of o-minimal group …
0
votes
0answers
184 views
Horizontal distribution of principal G bundle
If we consider $S^{2n-1}$->$\mathbb{CP}^{n-1}$ as a $S^1$ principal bundle, and given a connection 1-form as $C=\frac{1}{2\pi}\Sigma_i(x_i dx_i-y_i dy_i)$ (where $(x_1,y_1,...,x_{2 …
1
vote
1answer
224 views
is there an English translation of the book by Guy Barles?
is there an English translation of the book by Guy Barles, "Solutions de viscosite des equations de Hamiltion-Jacobi"? Springer-Verlag
0
votes
0answers
163 views
Faithful actions of finite groups on topological spaces
Suppose that $G$ is a finite group acting faithfully on a topological space $X$. In the smooth setting, one can deduce that for each $x$ in $M$, the induced map $$G_x \to Diff_x\le …
16
votes
4answers
1k views
Spectrum of the Grothendieck ring of varieties
Here's a problem that may ultimately require just simple algebraic-geometry skills to be solved, or perhaps it's very deep and will never be solved at all. From the comments, some …
2
votes
3answers
242 views
is there any efficient way to compute the follow matrix equations easily
Let $A$ and $D$ are $n\times n$ diagnal matrices, and $B$ is an $n\times n$ orthogonal matrix. Is there any efficient way to compute the follow matrix equations easily?
$\sum_{i=0 …
8
votes
2answers
883 views
What is the infinite-dimensional-manifold structure on the space of smooth paths mod thin homotopy?
This question is motivated by the recent paper An invitation to higher gauge theory by Baez and Huerta, and the 2007 paper Parallel Transport and Functors by Schreiber and Waldorf. …
7
votes
1answer
510 views
Lower bound on # of nonzero digits in ternary expansions of powers of 2?
Does anyone know of any lower bounds on the number of nonzero digits that appear in powers of 2 when written to base 3? (Other than the easy "If it's more than 8 it has to have at …
12
votes
2answers
845 views
topological “milnor’s conjecture” on torus knots.
Here's a question that has come up in a couple of talks that I have given recently.
The 'classical' way to show that there is a knot $K$ that is locally-flat slice in the 4-ball b …
1
vote
1answer
166 views
crookedness of convex curves (milnor)
hello,
I'm currently reading On the Total Curvature of Knots and am trying to understand one of the lemmas in it (3.3)
A closed polygon $P$ in $H^2$ is convex if and only if for …
1
vote
0answers
106 views
A bounded function of the packing and covering density of lattices
Given a (finite-dimensional) lattice $L$ of an Euclidean vector-space, the function
$$L\longmapsto -\log(\hbox{packing density of }L)/
\log(\hbox{covering density of }L)$$
is boun …
2
votes
2answers
535 views
Application of coordinate-stretching transformation for Perfectly Matched Layer
A Perfectly Matched Layer (PML) is an absorbing boundary condition (ABC) which can be used to approximate free-field conditions for the numerical solution of wave equation problems …
4
votes
1answer
397 views
failure of $\square(\kappa)$ at an inaccessible $\kappa$
How can we force the failure of $\square(\kappa)$ at an inaccessible $\kappa$, where
$\square(\kappa)$ is defined as follows: There is a sequence $(C_i:i< \kappa)$ such that:
…
6
votes
3answers
2k views
Simultaneous diagonalization
I'm pretty sure that the following (if true) is a standard result in linear algebra but unfortunately I could not find it anywhere and even worse I'm too dumb to prove it: Let $k$ …
0
votes
1answer
270 views
Convex sets and projections
Hello!
I recently started (it's purely self-education) reading a "Mathematical programming and optimizations" book, did a vast part of the exercises related to the theoretical par …
