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The Octonions
  • J. Baez
  • Mathematics, Physics
  • 17 May 2001
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics.Expand
Higher-Dimensional Algebra V: 2-Groups
A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various versions of thisExpand
Higher-Dimensional Algebra VI: Lie 2-Algebras
The theory of Lie algebras can be categorified starting from a new notion of '2-vector space', which we define as an internal category in Vect. There is a 2- category 2Vect having these 2-vectorExpand
Higher dimensional algebra and topological quantum field theory
The study of topological quantum field theories increasingly relies upon concepts from higher‐dimensional algebra such as n‐categories and n‐vector spaces. We review progress towards a definition ofExpand
Quantum geometry of isolated horizons and black hole entropy
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admittingExpand
Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes
Abstract We give a definition of weak n -categories based on the theory of operads. We work with operads having an arbitrary set S of types, or “ S -operads,” and given such an operad O , we denoteExpand
Spin foam models
  • J. Baez
  • Physics, Mathematics
  • 21 September 1997
While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define theExpand
From Finite Sets to Feynman Diagrams
Prediction is hard, especially when it comes to the future, but barring some unforeseen catastrophe, we can expect the amount of mathematics produced in the 21st century to dwarf that of all theExpand
Convenient Categories of Smooth Spaces
A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold,Expand
The 2010 Mw 8.8 Maule Megathrust Earthquake of Central Chile, Monitored by GPS
Using data from Global Positioning System networks in Central Chile to infer the static deformation and the kinematics of the 2010 moment magnitude 8.8 Maule megathrust earthquake, it is found that rupture reached shallow depths, probably extending up to the trench. Expand