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2013

2013

This paper is an introduction to relationships between quantum topology and quantum computing. We take a foundational approach…

Highly Cited

2010

Highly Cited

2010

We construct a genus one analogue of the theory of associators and the Grothendieck–Teichmüller (GT) group. The analogue of the…

2008

2008

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Please see the pdf file for the actual abstract and important remarks, which could not be put here due to the arXiv length…

Review

2006

Review

2006

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary…

2004

2004

Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular…

2003

2003

We introduce and develop a?language of semigroups over the braid groups to study the braid monodromy factorizations (bmf's) of…

Highly Cited

2000

Highly Cited

2000

We propose a general way of constructing set-theoretical solutions of the YangBaxter equation. We study the properties of the…

1993

1993

We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every…