# Tag Info

• 1,671
Accepted

### Twists, balances, and ribbons in pivotal braided tensor categories

Question 2: Given a pivotal braided category $\mathcal{C}$, there are 2 ways to endow $\mathcal{C}$ with twists under which $\mathcal{C}$ is a rigid balanced category. Conversely, given a rigid ...
• 5,097

### What's the right way to think about "anomalies" in 3d TQFTs?

Here is my understanding from physics point of view. A quantum field theory is anomalous if it lacks of a UV completion. In other words there is no lattice theory in the same dimension, whose ...
• 4,462

### Is the central charge of a Drinfeld center always 0?

The Drinfeld center of a spherical fusion category has topological central charge $0\pmod 8$ see Remark 5.19 in Müger, Michael: From subfactors to categories and topology. II. The quantum double ...
• 2,031
Accepted

• 1,395

### Gauss-Milgram formula for fermionic topological order?

We just posted a paper http://arxiv.org/abs/1507.04673 addressing this issue. For fermion topological orders, the fermionic version of this formula is $\Theta=\sum_a d_a^2 \theta_a=0$. See eq. 14 of ...
• 4,462
Accepted

### Bialgebras with rigid representation theory

Yes, it is true that if a quasi-Hopf algebra has a trivial coassociator, then it's equivalent to an actual Hopf algebra (with $\alpha=\beta=1$). In other words, if you know the category is rigid (i.e. ...
• 7,517

### Gauss-Milgram formula for fermionic topological order?

There is no fermionic analogue of the Gauss-Milgram formula. It applies to modular topological quantum field theories, while phases built out of fermions are not modular. A simple example, showing ...
• 152k
### Do $G$-invariant non-degenerate quadratic forms come from $G$-invariant even lattices?
The group of automorphisms of $A$ which preserve the quadratic form $q$ is known as the orthogonal group $O(A,q)$. Likewise, if $L$ is a free $\mathbb{Z}$-module of finite rank with an even \$\mathbb{...