Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Douglas, Christopher L"'
Diagrammatic notation has become a ubiquitous computational tool; early examples include Penrose's graphical notation for tensor calculus, Feynman's diagrams for perturbative quantum field theory, and Cvitanovic's birdtracks for Lie algebras. Categor
Externí odkaz:
http://arxiv.org/abs/2208.13758
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial topology with a
Externí odkaz:
http://arxiv.org/abs/2112.14700
We prove that finite-index conformal nets are fully dualizable objects in the 3-category of conformal nets. Therefore, assuming the cobordism hypothesis applies, there exists a local framed topological field theory whose value on the point is any fin
Externí odkaz:
http://arxiv.org/abs/1905.03393
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.
Externí odkaz:
http://arxiv.org/abs/1812.11933
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 897-956
Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we introduced a not
Externí odkaz:
http://arxiv.org/abs/1605.00662
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global dimension in eac
Externí odkaz:
http://arxiv.org/abs/1509.06811
Autor:
Douglas, Christopher L
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 133-137).
There are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a
Includes bibliographical references (p. 133-137).
There are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a
Externí odkaz:
http://hdl.handle.net/1721.1/33095
A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and modularity conditions.
Externí odkaz:
http://arxiv.org/abs/1411.0945
Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topologi
Externí odkaz:
http://arxiv.org/abs/1409.8672