arXiv subjects

Qi Chen

Publications and source records attributed to Qi Chen.

328 records · Page 19Linked to original sources

arXiv2007

Higher Rank TQFT Representations of SL(2,Z) are Reducible

In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the symmetry which exchanges SU(N) representation labels by their conjugates. The respective summands of a given parity are typically still reducible into many further components. Specifically, we give an explicit basis for an irreducible direct summand in the SL(2,Z) representation obtained from quantum PSU(3) when the order of the root of unity is a prime r=2 mod 3. We show that this summand is isomorphic to the respective PSU(2) representation.

math.GT↗

arXiv2005

Almost integral TQFTs from simple Lie algebras

Almost integral TQFTs were introduced by Gilmer [Duke Math. J. 125 (2004) 389--413]. The aim of this paper is to modify the TQFT of the category of extended 3-cobordisms given by Turaev (in his book: Quantum invariants of knots and 3-manifolds) to obtain an almost integral TQFT.

math.QA↗

arXiv2004

Quantum Invariants of Periodic Links and Periodic 3-Manifolds

We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincare sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.

math.QA↗

arXiv2004

On certain integral tensor categories and integral TQFTs

We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these categories.

math.QA↗