arXiv subjects

Hao Zheng

Publications and source records attributed to Hao Zheng.

293 records · Page 17Linked to original sources

arXiv2006

General cycling operations in Garside groups

In this article, we introduce the notion of cycling operations of arbitrary order in Garside groups, which is a full generalization of the cycling and decycling operations. Theoretically, this notion together with other related concepts provides a context in which various definitions and arguments concerning Garside groups are unified and simplified as well as improved. Practically, it yields a new algorithm which has a considerably improved performance on solving the conjugacy problem of reducible braids.

math.GT↗

arXiv2006

Proof of the volume conjecture for Whitehead doubles of a family of torus knots

A technique to calculate the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then we prove the volume conjecture for Whitehead doubles of a family of torus knots and show some interesting observations.

math.GT↗

arXiv2006

On the Hecke algebras and the colored HOMFLY polynomial

This paper has been withdrawn since it is identical to the paper math.QA/0601267. It was posted by mistake.

math.QA↗

arXiv2006

On the Hecke algebras and the colored HOMFLY polynomial

The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mariño-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links.

math.QA↗

arXiv2005

Faithfulness of the Lawrence representation of braid groups

The Lawrence representation $L_{n,m}$ is a family of homological representation of the braid group $B_n$, which specializes to the reduced Burau and the Lawrence-Krammer representation when $m$ is 1 and 2. In this article we show that the Lawrence representation is faithful for $m \geq 2$.

math.GT↗