13,978 reputation
142104
bio website sbseminar.wordpress.com
location Bloomington, Indiana
age 34
visits member for 5 years, 7 months
seen 26 mins ago
Assistant Professor at Indiana University, working on tensor categories and their relationships to operator algebras and topology.

Mar
31
comment Nilpotence of the stable Hopf map via framed cobordism
The 12 seems to big to be easily geometrically explained, but it's enough to just show that the 3-torus is cobordant to $M \coprod M$ for some 3-manifold M.
Mar
31
comment Nilpotence of the stable Hopf map via framed cobordism
@QiaochuYuan: You're right, I forgot that there were primes other than 2. (Or rather, I was looking at the picture for just the 2-part.)
Mar
31
comment Nilpotence of the stable Hopf map via framed cobordism
A closely related fact, which quickly implies this one, is that the 3-torus is cobordant to a disjoint union of four copies of the 3-sphere (with its unit quaternion framing). Since that's just 3-dimensional it might be easier to see.
Mar
31
awarded  Nice Question
Mar
31
asked Nilpotence of the stable Hopf map via framed cobordism
Mar
25
awarded  Popular Question
Mar
15
awarded  Good Answer
Feb
22
awarded  Good Answer
Feb
17
comment How to proceed with a type-theoretic proof that $\Sigma \mathbb{S}^1 \simeq \mathbb{S}^2$?
I'm a bit confused about what your definition of $\Sigma S^1$ is. I would have expected it to be generated by one point, one 1-loop, and two 2-paths trivializing the 1-loop. But you seem to have two points. Could you clarify your notation a little?
Feb
15
comment In a closed monoidal abelian category, are the compact projectives a monoidal subcategory?
If your tensor category is finite, then compact projective is the same as projective. In that setting, tensoing a projective by anything is projective, see Prop 2.1 of arxiv.org/abs/math/0301027
Feb
8
comment Has a subfactor with lattice $B_3$, a singly generated identity biprojection?
In the group/subgroup case what group theoretical statement does this correspond to?
Jan
18
awarded  Good Question
Jan
13
answered Relationship between Hochschild cohomology and Drinfeld centers
Jan
8
accepted Is there a “simplification” functor in algebraic topology?
Jan
8
awarded  Nice Question
Jan
8
comment Is there a “simplification” functor in algebraic topology?
@QiaochuYuan: Ah, ok, I'd just assumed that $B(G/[G,G])$ was a simplification of BG, but I see what you're saying (the perfect space Y is just the Eilenberg-MacLane space corresponding to the nontrivial cohomology). Probably $B(A_5)$ is already a problem.
Jan
8
revised Is there a “simplification” functor in algebraic topology?
Connected
Jan
8
comment Is there a “simplification” functor in algebraic topology?
Yes, in the homotopy category.
Jan
8
asked Is there a “simplification” functor in algebraic topology?
Dec
24
revised Why does a tetracategory with one object, one 1-morphism and one 2-morphism give a symmetric monoidal category
added 59 characters in body