Exact Computation of the n-Loop Invariants of Knots
نویسندگان
چکیده
The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in 1/N . We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power series of a knot. We give examples that illustrate our method and its results.
منابع مشابه
Knots , Links and Branes at Large N
We consider Wilson loop observables for Chern-Simons theory at large N and its topological string dual and extend the previous checks for this duality to the case of links. We find an interesting structure involving representation/spin degeneracy of branes ending on branes which features in the large N dual description of Chern-Simons theory. This leads to a refinement of the integer invariants...
متن کاملDimensions of Spaces of Finite Type invariants of Virtual Knots
The study of finite type invariants is central to the development of knot theory. Much of the theory still needs to be extended to the newer virtual context. In this article we calculate the dimensions of the spaces of virtual finite type knot invariants and associated graded algebras for several classes of virtual knots to orders four and five. The data obtained highlights a certain pattern on...
متن کاملExtended knots and the space of states of quantum gravity
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions has been traditionally based upon geometric (in contrast to analytic) properties of the loops. The reason for this preferred way is twofold: for one hand th...
متن کاملNew Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
متن کاملSome Invariants of Pretzel Links
Abstract. We show that nontrivial classical pretzel knots L(p, q, r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of npretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links by showing that the genus and the canonical genus of a pretzel link...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Experimental Mathematics
دوره 25 شماره
صفحات -
تاریخ انتشار 2016