bio  website  math.psu.edu/petrunin 

location  Penn State  
age  46  
visits  member for  5 years, 3 months 
seen  1 hour ago  
stats  profile views  10,991 
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 
Continuouspiecewiselinear versus piecewiselinear
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, Hprinciple 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 piecewiselinear homeomorphisms
deleted 8 characters in body 
Dec 25 
revised 
Nonperiodic points of piecewiselinear 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 