• Corpus ID: 252568135

The Y-Product

@inproceedings{Kwon2022TheY,
  title={The Y-Product},
  author={Alice Kwon and Ying Hong Tham},
  year={2022}
}
. We present a topological construction that provides many examples of non-commutative Frobenius algebras that generalizes the well-known pair-of-pants. When applied to the solid torus, in conjunction with Crane-Yetter theory, we provide a topological proof of the Verlinde formula. We also apply the construction to a solid handlebody of higher genus, leading to a generalization of the Verlinde formula (not the higher genus Verlinde formula); in particular, we define a generalized S -matrix… 

References

SHOWING 1-10 OF 18 REFERENCES

On fusion categories

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show

Observables in the Turaev-Viro and Crane-Yetter models

We define an invariant of graphs embedded in a 3-manifold and a partition function for 2-complexes embedded in a triangulated 4-manifold by specifying the values of variables in the Turaev-Viro and

The finiteness conjecture for skein modules

We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that skein modules of closed 3-manifolds are

Invariants of links of Conway type

The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial

On the Structure of Modular Categories

For a braided tensor category C and a subcategory K there is a notion of a centralizer CC K, which is a full tensor subcategory of C. A pre‐modular tensor category is known to be modular in the sense

Morse theory for manifolds with boundary

We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a

A Morse complex on manifolds with boundary

Given a compact smooth manifold M with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology

A polynomial invariant for knots via von Neumann algebras

Thus, the trivial link with n components is represented by the pair (l ,n), and the unknot is represented by (si$2 * * • s n i , n) for any n, where si, $2, • • • > sn_i are the usual generators for

String-net model of Turaev-Viro invariants

The relation between the Turaev--Viro TQFT and the string-net space introduced in the papers of Levin and Wen and the case of surfaces with boundary is considered in detail.