14
votes
Accepted
Relation between the homotopy classes of maps on a torus, and maps on a sphere
One case in which you can establish a simple relationship is when $Y$ is a loop space. Suppose that $Y\simeq \Omega Z=\mbox{map}_*(S^1, Z)$. Then there is a bijection $[{\mathbb T}^d, Y]_*\cong [\...
- 10.9k
13
votes
Accepted
Are framed manifolds cubulatable?
If you glue together the Riemannian metrics on the various cubes you obtain a flat metric on your cubulated manifold. So e.g. $S^3\cong SU(2)$ is framed but not cubulated.
- 40.2k
12
votes
Accepted
Is there a simple argument that shows that two unitary fusion categories are Morita equivalent if their Drinfeld centers are equal?
In the non-unitary setting ENO proved that if $Z(C)$ and $Z(D)$ are equivalent as braided tensor categories, then C and D are Morita equivalent. This is Theorem 3.1 of this paper. Note that they ...
- 28.1k
6
votes
Accepted
Generalization of Drinfeld double to comodule algebras
Such an algebra exists. As far as I am aware, the algebra was first described in chapter 6 of The blob complex by Morrison and Walker. In this paper, the algebra is construct from a diagrammatic ...
- 3,830
4
votes
Accepted
Relationship between irreducible representations of the Schur covering group and elements of $H^2(G,U(1))$
The answer to your question is Yes. Consider your covering group $C$ as a central extension:
$$1 \to N \to C \to G \to 1$$
and suppose it is given by a 2-cocycle $\alpha \in H^2(G, N)$. Then for any ...
- 45.7k
3
votes
Generalization of Drinfeld double to comodule algebras
I think Davydov's papers Centre of an algebra and Full centre of an H-module algebra might be what you are looking for.
- 54.6k
3
votes
Vorticial ground states for the O(2) rotor model
I think your question is interesting and reasonable. But I don't know the answer, so I'll say something else.
Kosterlitz and Thouless won the physics Nobel prize this week for their work on this ...
- 22.3k
3
votes
Q-Gaussian processes and probability space
There is no classical $L^2$-space which would do this, as multiplication with the field operators does not commute. However, the $q$-Fock space $\cal{F}_q(\cal{H})$ is to be considered as this ...
- 1,210
3
votes
What is the etale homotopy type of the Witt group of braided fusion categories?
The answers to your questions are essentially in the first paper you cite. The second paper has more information on finer structure, like torsion, but the basic properties are all we need.
In the ...
- 45.7k
2
votes
Accepted
Supersymmetric SYK Model in 3D?
The disordered SYK model in three dimensions with supersymmetry was studied by Fedor Popov in Supersymmetric tensor model at large $N$ and small $\varepsilon$.
The complications are discussed in A 3d ...
- 188k
2
votes
Generalization of Drinfeld double to comodule algebras
Section 1 (in particular Prop 1.23) of On module categories over finite-dimensional Hopf algebras by Andruskiewitsch-Mombelli come close to an answer to your question: namely, they show that if $H$ is ...
- 8,524
2
votes
What is a Fermi surface?
Quoting p. 142 of the trusty Ashcroft-Mermin (who write $\mathcal E_F$ for your $\mu$):
For each partially filled band there will be a surface in $k$-space separating the occupied from the ...
- 31.5k
1
vote
Relation between the homotopy classes of maps on a torus, and maps on a sphere
It would be interesting if the paper
"Homotopy Groups and Torus Homotopy Groups",
Ralph H. Fox,
Annals of Mathematics,
Second Series, Vol. 49, No. 2 (Apr., 1948), pp. 471-510,
could be seen as ...
- 12.3k
1
vote
Regularizing divergent sums over lattices
As far as I know, renormalization in Physics works just the way it does in analytic number theory. Our problematic series:
$$ \sum_{n=1}^\infty a_n = \infty $$
can be regularized by adding only ...
- 22.8k
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