科研之友
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摘要
Recent advances in Quantum Topology assign -series to knots in at least three different ways. The -series are given by generalized Nahm sums (i.e., special -hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those -series that come from planar graphs (i.e., reduced Tait graphs of alternating links) and compute several terms of those series for all graphs with at most 8 edges drawing several conclusions. In addition, we give a graph-theory proof of a theorem of Dasbach-Lin which identifies the coefficient of in those series for in terms of polynomials on the number of vertices, edges, and triangles of the graph.
- 出版日期2015-4
