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We compute the RO(G)‐graded equivariant algebraic K‐groups of a finite field with an action by its Galois group G. Specifically, we show these K‐groups split as the sum of an explicitly computable term and the well‐studied RO(G)‐graded coefficient groups of the equivariant Eilenberg–MacLane spectrum HZ. Our comparison between the equivariant K‐theory spectrum and HZ further shows they share the same Tate spectra and geometric fixed point spectra. In the case where G has prime order, we provide an explicit presentation of the equivariant K‐groups.more » « less
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We define a monoidal category W and a closely related 2‐category 2Weyl using diagrammatic methods. We show that 2Weyl acts on the category TL of modules over Temperley–Lieb algebras, with its generating 1‐morphisms acting by induction and restriction. The Grothendieck groups of W and a third category we define W^\infty are closely related to the Weyl algebra. We formulate a sense in which K_0(W^\infty) acts asymptotically on K_0(TL).more » « less
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We use the degree of the colored Jones knot polynomials to show that the crossing number of a (p,q)‐cable of an adequate knot with crossing number c is larger than q^2 c. As an application, we determine the crossing number of 2‐cables of adequate knots. We also determine the crossing number of the connected sum of any adequate knot with a 2‐cable of an adequate knot.more » « less
