QuantumAlgebraicTopologyTopics 2009-02-02 19:20:32 2009-02-02 19:28:04 Topic quantum algebraic topology: % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % define commands here \usepackage{amsmath, amssymb, amsfonts, amsthm, amscd, latexsym} \usepackage{xypic} \usepackage[mathscr]{eucal} \theoremstyle{plain} \newtheorem{lemma}{Lemma}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[section] \theoremstyle{definition} \newtheorem{definition}{Definition}[section] \newtheorem{example}{Example}[section] %\theoremstyle{remark} \newtheorem{remark}{Remark}[section] \newtheorem*{notation}{Notation} \newtheorem*{claim}{Claim} \renewcommand{\thefootnote}{\ensuremath{\fnsymbol{footnote%%@ }}} \numberwithin{equation}{section} \newcommand{\Ad}{{\rm Ad}} \newcommand{\Aut}{{\rm Aut}} \newcommand{\Cl}{{\rm Cl}} \newcommand{\Co}{{\rm Co}} \newcommand{\DES}{{\rm DES}} \newcommand{\Diff}{{\rm Diff}} \newcommand{\Dom}{{\rm Dom}} \newcommand{\Hol}{{\rm Hol}} \newcommand{\Mon}{{\rm Mon}} \newcommand{\Hom}{{\rm Hom}} \newcommand{\Ker}{{\rm Ker}} \newcommand{\Ind}{{\rm Ind}} \newcommand{\IM}{{\rm Im}} \newcommand{\Is}{{\rm Is}} \newcommand{\ID}{{\rm id}} \newcommand{\GL}{{\rm GL}} \newcommand{\Iso}{{\rm Iso}} \newcommand{\Sem}{{\rm Sem}} \newcommand{\St}{{\rm St}} \newcommand{\Sym}{{\rm Sym}} \newcommand{\SU}{{\rm SU}} \newcommand{\Tor}{{\rm Tor}} \newcommand{\U}{{\rm U}} \newcommand{\A}{\mathcal A} \newcommand{\Ce}{\mathcal C} \newcommand{\D}{\mathcal D} \newcommand{\E}{\mathcal E} \newcommand{\F}{\mathcal F} \newcommand{\G}{\mathcal G} \newcommand{\Q}{\mathcal Q} \newcommand{\R}{\mathcal R} \newcommand{\cS}{\mathcal S} \newcommand{\cU}{\mathcal U} \newcommand{\W}{\mathcal W} \newcommand{\bA}{\mathbb{A}} \newcommand{\bB}{\mathbb{B}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bD}{\mathbb{D}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bG}{\mathbb{G}} \newcommand{\bK}{\mathbb{K}} \newcommand{\bM}{\mathbb{M}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bO}{\mathbb{O}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bV}{\mathbb{V}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\bfE}{\mathbf{E}} \newcommand{\bfX}{\mathbf{X}} \newcommand{\bfY}{\mathbf{Y}} \newcommand{\bfZ}{\mathbf{Z}} \renewcommand{\O}{\Omega} \renewcommand{\o}{\omega} \newcommand{\vp}{\varphi} \newcommand{\vep}{\varepsilon} \newcommand{\diag}{{\rm diag}} \newcommand{\grp}{{\mathbb G}} \newcommand{\dgrp}{{\mathbb D}} \newcommand{\desp}{{\mathbb D^{\rm{es}}}} \newcommand{\Geod}{{\rm Geod}} \newcommand{\geod}{{\rm geod}} \newcommand{\hgr}{{\mathbb H}} \newcommand{\mgr}{{\mathbb M}} \newcommand{\ob}{{\rm Ob}} \newcommand{\obg}{{\rm Ob(\mathbb G)}} \newcommand{\obgp}{{\rm Ob(\mathbb G')}} \newcommand{\obh}{{\rm Ob(\mathbb H)}} \newcommand{\Osmooth}{{\Omega^{\infty}(X,*)}} \newcommand{\ghomotop}{{\rho_2^{\square}}} \newcommand{\gcalp}{{\mathbb G(\mathcal P)}} \newcommand{\rf}{{R_{\mathcal F}}} \newcommand{\glob}{{\rm glob}} \newcommand{\loc}{{\rm loc}} \newcommand{\TOP}{{\rm TOP}} \newcommand{\wti}{\widetilde} \newcommand{\what}{\widehat} \renewcommand{\a}{\alpha} \newcommand{\be}{\beta} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\de}{\delta} \newcommand{\del}{\partial} \newcommand{\ka}{\kappa} \newcommand{\si}{\sigma} \newcommand{\ta}{\tau} \newcommand{\lra}{{\longrightarrow}} \newcommand{\ra}{{\rightarrow}} \newcommand{\rat}{{\rightarrowtail}} \newcommand{\oset}[1]{\overset {#1}{\ra}} \newcommand{\osetl}[1]{\overset {#1}{\lra}} \newcommand{\hr}{{\hookrightarrow}} This is a new, contributed topic on quantum algebraic topology. {\bf [Additions are in progress]} \section{Quantum Algebraic Topology (QAT) Topics} \emph{Quantum algebraic topology} can be described as the area of mathematical physics and physical mathematics concerned with the application of algebraic topology concepts, procedures and results to quantum theories such as quantum field theories (QFT, AQFT, locally covariant relativististic quantum theories and quantum gravity (QG)). QAT has close connections to several other fundamental fields of mathematics, such as: noncommutative geometry (NCG), the theory of categories, functors and natural transformations (TCFN), non-Abelian algebraic topology (NAAT), and higher dimensional algebra (HDA). Related references are available at the websites and documents in the following topics list. \subsection{QAT Topics : Online Resources} \begin{itemize} \item \item QAT: \PMlinkexternal{Quantum Algebraic Topology-preprint}{http://planetmath.org/?op=getobj&from=lec&id=68}. \item AT: \PMlinkexternal{Algebraic Topology papers}{http://www.bangor.ac.uk/~mas010/publicfull.htm} \item NAAT: \PMlinkexternal{A first textbook on ``Non-Abelian Algebraic Topology''}{http://www.bangor.ac.uk/~mas010/nonab-a-t.html} \item QA: \PMlinkname{Quantum automata and quantum supercomputers}{QuantumAutomataAndQuantumComputation2} \item NAQAT: \PMlinkexternal{Non-Abelian QAT}{http://www.bangor.ac.uk/~mas010/pdffiles/BBG-158-NAC0STQG.pdf} \item NAAT-List: \PMlinkexternal{Category Theory, Homotopy Theory and AT Publications}{http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/07/cathom07.html} \item SPE: \PMlinkexternal{Stanford Plato: Category Theory and Applications}{http://plato.stanford.edu/entries/category-theory/} \item Abc \end{itemize} \begin{thebibliography}{9} \bibitem{Abstracts1} Abstracts1: \PMlinkexternal{Springer link}{http://www.springerlink.com/content/t08637r333403846/} \bibitem{Abstracts2} Abstracts2: \PMlinkexternal{Springer link}{http://www.springerlink.com/content/92r13230n3381746/} \bibitem{ICB2k4} CERN Preprint Archives: \PMlinkexternal{CERN Preprints-1}{http://documents.cern.ch/cgi-bin/setlink?base=preprint&categ=ext&id=ext-2004-125} \bibitem{ICB2k5} CERN Articles and Preprint Archives: \PMlinkexternal{CERN Preprints-2}{http://doc.cern.ch/archive/electronic/other/ext/ext-2004-125/Baianu_okCERNMyPreprintsJuly9k04.doc} \end{thebibliography} \subsection{Additional items} \begin{enumerate} \item QAT1 \item QAT2 \item A3 \end{enumerate}