non-Abelian Quantum Algebraic Topology NONABELIANQUANTUMALGEBRAICTOPOLOGY2 2010-09-28 01:45:05 2010-09-28 02:06:10 Topic quantum algebraic topology non-Abelian quantum algebra algebraic topology quantum gravity \section{non-Abelian Quantum Algebraic Topology} This is a new contributed topic (under construction). \emph{Quantum Algebraic Topology} is the area of theoretical physics and physical mathematics concerned with the applications of Algebraic Topology methods, results and constructions (including its extensions to Category Theory, Topos Theory and Higher Dimensional Algebra) to fundamental quantum physics problems, such as the representations of Quantum spacetimes and Quantum State Spaces in Quantum Gravity, in arbitrary reference frames. Non--Abelian gauge field theories can also be formalized or presented in the QAT framework. Perhaps the neighbor areas with which QAT overlaps significantly are: Algebraic Quantum Field Theories (AQFT)/Local Quantum Physics (LQP), Axiomatic QFT, Lattice QFT (LQFT) and Supersymmetry/Supergravity. One can also claim overlap with various Topological Field Theories (TFT), or Topological ‘Quantum’ Field Theories (TQFT), Homotopy QFT (HQFT), Dilaton, and Lattice Quantum Gravity (respectively, DQG and LQG) theories.