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Infinity Links L, infinity-4-Manifolds M_L and Kirby Categories | | Renaud Gauthier
; | | Date: |
29 Sep 2013 | | Abstract: | We construct what we call a Kirby category, a monoidal category whose
morphisms are smooth 4-manifolds, projecting down to another monoidal category
whose morphisms are orientable 3-manifolds, the projection being induced by the
boundary map on manifolds. We construct a higher categorical generalization of
such concepts and introduce the notion of ribbon $infty$-categories, a
generalization of braided monoidal $infty$-categories (cite{Lu1}), which
gives rise to the concepts of $infty$-links, $infty$-4-manifolds as well as
the more general notion of walled $infty$-4-manifolds if one focuses attention
on $infty$-4-manifolds built from gluing thickened sheets on ribbons. These
fall into a larger class of constrained $infty$-4-manifolds whose classical
4-dimensional counterparts are constrained 4-manifolds on which we consider
physical theories. We regard pairs of constrained 4-manifolds and Lagrangians
densities depicting physical theories defined on such spaces as morphism
objects in an enhanced Kirby category, whose objects are regarded as events. We
define a universal category $Lambda$ of all events that we relate to the
$infty$-category of ribbon $infty$-categories and conclude in part that
Lagrangian field theories can be superseded by using $infty$-categories. | | Source: | arXiv, 1309.7514 | | Services: | Forum | Review | PDF | Favorites | |
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