Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Joao Faria"'
We give a simple, geometric and explicit construction of 3d untwisted Dijkgraaf-Witten theory with defects of all codimensions. It is given as a symmetric monoidal functor from a defect cobordism category into the category of finite-dimensional compl
Externí odkaz:
http://arxiv.org/abs/2410.18049
In a previous paper by one of the authors, a Lagrangian 3-form structure was established for a generalised Darboux system, originally describing orthogonal curvilinear coordinate systems, which encodes the Kadomtsev-Petviashvili (KP) hierarchy. Here
Externí odkaz:
http://arxiv.org/abs/2305.03182
Autor:
Martins, João Faria, Porter, Timothy
We first revisit the construction of Quinn's Finite Total Homotopy TQFT, which depends on the choice of a homotopy finite space, $\boldsymbol{B}$. We build our construction directly from homotopy theoretical techniques, and hence, as in Quinn's origi
Externí odkaz:
http://arxiv.org/abs/2301.02491
We define an exactly solvable model for 2+1D topological phases of matter on a triangulated surface derived from a crossed module of semisimple finite-dimensional Hopf algebras, the `Hopf-algebraic higher Kitaev model'. This model generalizes both th
Externí odkaz:
http://arxiv.org/abs/2104.02766
Publikováno v:
Comm. Math. Phys. 402, 1621-1705 (2023)
Here $\underline{M}$ denotes a pair $(M,A)$ of a manifold and a subset (e.g. $A=\partial M$ or $A=\emptyset$). We construct for each $\underline{M}$ its motion groupoid $\mathrm{Mot}_{\underline{M}}$, whose object set is the power set $ {\mathcal P}
Externí odkaz:
http://arxiv.org/abs/2103.10377
Each pointed topological space has an associated $\pi$-module, obtained from action of its first homotopy group on its second homotopy group. For the $3$-ball with a trivial link with $n$-components removed from its interior, its $\pi$-module $\mathc
Externí odkaz:
http://arxiv.org/abs/1912.11898
Publikováno v:
Advances in Theoretical and Mathematical Physics Volume 23 (2019) Number 7
We show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call W-bikoids (weld
Externí odkaz:
http://arxiv.org/abs/1807.09551
Publikováno v:
Reviews in Mathematical Physics, Vol. 32, No. 04, 2050011 (2020)
Higher gauge theory is a higher order version of gauge theory that makes possible the definition of 2-dimensional holonomy along surfaces embedded in a manifold where a gauge 2-connection is present. In this paper, we will continue the study of Hamil
Externí odkaz:
http://arxiv.org/abs/1702.00868
Autor:
Martins, Joao Faria, Picken, Roger
Publikováno v:
Homology, Homotopy & Applications . 2015, Vol. 17 Issue 2, p205-233. 29p
We define an invariant of tangles and framed tangles given a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying natural properties. We give several examples of Reidemeister pairs derived from racks, quandles, rack a
Externí odkaz:
http://arxiv.org/abs/1612.03501
Publikováno v:
Phys. Rev. B 95, 155118 (2017)
We propose an exactly solvable Hamiltonian for topological phases in $3+1$ dimensions utilising ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a Hamiltonian realisat
Externí odkaz:
http://arxiv.org/abs/1606.06639