Reputation
8,025
Next privilege 10,000 Rep.
Access moderator tools
Badges
1 32 88
Impact
~127k people reached

May
3
revised Appropriate morphisms and 2-morphisms in Ind(C)
shrunk image
Apr
29
revised Appropriate morphisms and 2-morphisms in Ind(C)
Finally, a picture.
Apr
28
answered Appropriate morphisms and 2-morphisms in Ind(C)
Apr
24
revised Efficient CW structures on squarefree semi-algebraic set
clarification on coefficients
Apr
24
asked Efficient CW structures on squarefree semi-algebraic set
Apr
23
answered discrete Grothendieck construction
Apr
21
comment What's known about the stalks of Lusztig's perverse sheaves on quiver varieties?
@BenWebster how could you forget, it's only been six years!
Apr
20
comment What's known about the stalks of Lusztig's perverse sheaves on quiver varieties?
For others who don't wish head-butt the inevitable jstor paywall when searching for Lusztig's paper: webpages.math.luc.edu/~ptingley/oldseminars/…
Apr
16
comment Examples of combinatorial bijections found by considering functors
This question, while interesting, is extremely broad in scope. An enormous family of examples comes just from the topological invariance of Euler characteristic! Are you simply looking for successful examples of categorification, or is there a more specific purpose to your question?
Apr
15
revised Discrete Morse theory: how do zig-zag paths determine homotopy type?
Added summary for tl;dr people
Apr
11
comment Discrete Morse theory: how do zig-zag paths determine homotopy type?
@Leon Take your time. But also make sure you go through Liviu's excellent "Tame flows", which was an inspiration for this preprint and has been duly cited...
Apr
11
revised Discrete Morse theory: how do zig-zag paths determine homotopy type?
Changed to OP's notation, replacing \Sigma by \cal{M}.
Apr
11
comment Discrete Morse theory: how do zig-zag paths determine homotopy type?
If there are no zigzag paths of the form $$ c > y_0 < x_0 > y_1 < x_1 > \cdots > y_k < x_k > c' $$ where $c$ and $c'$ are critical $7$ and $5$-dimensional simplices while $(y_\bullet < x_\bullet)$ lie in $\mathcal{M}$, then you definitely have homotopy equivalence with the wedge of spheres. Just be careful that all $>$ signs in the paths indicate "face of", not just "codimension 1 face" as in Forman's description. This will follow either from Liviu's answer or mine.
Apr
11
comment Discrete Morse theory: how do zig-zag paths determine homotopy type?
Liviu, great answer! But I think you mean "Forman" instead of "Foreman" in many places...
Apr
11
answered Discrete Morse theory: how do zig-zag paths determine homotopy type?
Apr
11
comment Classifying countable sets of weighted dots on a real line
Also, just to see if I get the rules: if we have "all positive integers, zero and all halved negative integers", how would you find an equivalent representative with only positive dots? Let's say all weights are 1.
Apr
11
comment Classifying countable sets of weighted dots on a real line
How intriguing. While we think about it, could you please explain briefly why this gadget is of interest to you?
Apr
10
awarded  Good Question
Apr
8
comment What word can I use for a poset with equivalences
So is the pro-proset set empty?
Apr
8
accepted How many simplicial complexes on n vertices up to homotopy equivalence?