منابع مشابه
Twisted Duality for Embedded Graphs
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge, and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 |E(G)|, the ribbon group, on G. The action of the ribbon group on embedded graphs extends the concepts of duality, partial duality, and Petrie duality. We show that th...
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We consider two operations on the edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 e(G), the ribbon group of G, on G. We show that this ribbon group action gives a complete characterization of duality in that if G is any cellularly embedded graph wit...
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Let G be a directed graph embedded in a surface. A map φ : E(G) → R is a tension if for every circuit C ⊆ G, the sum of φ on the forward edges of C is equal to the sum of φ on the backward edges of C. If this condition is satisfied for every circuit of G which is a contractible curve in the surface, then φ is a local tension. If 1 ≤ |φ(e)| ≤ α − 1 holds for every e ∈ E(G), we say that φ is a (l...
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Let the discrete group G act properly and isometrically on the Riemannian manifold X. Let C0(X, δ) be the section algebra of a smooth locally trivial G-equivariant bundle of elementary C∗-algebras representing an element δ of the Brauer group BrG(X). Then C0(X, δ ) ⋊ G is KK-theoretically Poincaré dual to ( C0(X, δ)⊗̂C0(X)Cτ (X) ) ⋊ G, where δ is the inverse of δ in the Brauer group. We deduce t...
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The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms toge...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2012
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05529-7