18,008 reputation
359142
bio website math.psu.edu/petrunin
location Penn State
age 46
visits member for 5 years, 3 months
seen 1 hour ago

A description from my son:

Mein Vater hat keine Haare aber er hat einen schwarzen Bart. Er hat grüne Augen so wie ich. Er benutzt seine Brille sehr selten. Sein Name ist Tosha. Er mag Musik spielen aber ist ganz schlecht dabei und ist 44 Jahre alt.


1d
comment When is a homogeneous space connected?
The group $H/(H\cap G_0)$ can be considered as a subgroup in $G/G_0$. The space is connected if $H/(H\cap G_0)=G/G_0$. Assume $G/G_0=\mathbb Z$ and $H/(H\cap G_0)=2{\cdot}\mathbb Z$; they are isomorphic but the space has two connected components. (Maybe you want to assume that $G$ is compact?)
Jan
28
awarded  Notable Question
Jan
26
comment Continuous-piecewise-linear versus piecewise-linear
For the finite or locally finite complexes PL=CPL. So the difference might appear only in the weird part of our world and it requires more defs to see it.
Jan
21
answered Whether the manifold part of an Alexandrov space is connected?
Jan
21
comment Canonical Immersion of the Double Torus
Each harmonic form gives you a map to $\mathbb S^1$; you can take a basis for harmonic forms and map your surface in an $n$-torus, the later can be embedded into $\mathbb R^{2{\cdot}n}$ if you want. This embedding is not isometric, but it is kind of canonical; so maybe something can be build on it.
Jan
19
answered Convex subcomplexes of CAT(0) cubical complexes
Jan
14
comment Your favorite surprising connections in Mathematics
@semyonalesker: thank you, it is corrected now.
Jan
14
revised Your favorite surprising connections in Mathematics
edited body
Jan
14
awarded  Good Answer
Jan
6
comment Isotopy of positively curved surfaces of revolution in $\mathbb{R}^3$
@user64672, yes, any open invariant condition will do; for example we could say that the principle curvatures strictly pinched by given constants.
Jan
6
comment Isotopy of positively curved surfaces of revolution in $\mathbb{R}^3$
@user64672: In this case, H-principle says that we can start with any isotopy and deform it (rel. ends) into positively curved one.
Jan
5
answered Isotopy of positively curved surfaces of revolution in $\mathbb{R}^3$
Dec
30
comment Shortest rope to capture a sphere of diameter 1
@AndréHenriques, apparently this is not optimal.
Dec
25
comment A question about a manifold in an $n$-dimensional Alexandrov space with curvature bounded below
@LewisZang: If boundary is not empty, you can pass to the doubling; this should solve the problem.
Dec
25
revised Nonperiodic points of piecewise-linear homeomorphisms
deleted 8 characters in body
Dec
25
revised Nonperiodic points of piecewise-linear homeomorphisms
update
Dec
24
revised Is there Domain Invariance for Alexandrov spaces?
remove \\
Dec
24
comment A question about a manifold in an $n$-dimensional Alexandrov space with curvature bounded below
See mathoverflow.net/questions/21512.
Dec
23
comment Distance function to a submanifold
@user64231, right, for distance function it is easier. In general, you may cover almost all $M$ by charts such that gradient $f$ is almost constant. Then move in the coordinate direction of such chart.
Dec
23
revised Distance function to a submanifold
added 372 characters in body