Knot state asymptotics I: AJ conjecture and Abelian representations
نویسندگان
چکیده
منابع مشابه
Knot state asymptotics I AJ Conjecture and abelian representations
Consider the Chern-Simons topological quantum field theory with gauge group SU2 and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vector space. We call this vector the knot state and study its asymptotic properties when the level is large. The latter vector space being isomorphic to the geometric quantization of the SU2-character variety of t...
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The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (−2, 3, 6n ± 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r, 2)-cables of a knot, where r is an odd integer. In particular, we show tha...
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In the context of the Batalin-Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander-Conway polynomial. The three-dimensional case is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula for the second coefficient of the Alexander-Conway polyn...
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ژورنال
عنوان ژورنال: Publications mathématiques de l'IHÉS
سال: 2015
ISSN: 0073-8301,1618-1913
DOI: 10.1007/s10240-015-0068-y