This is a new, contributed topic on Quantum Algebraic Topology. 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. \item QAT: Quantum Algebraic Topology-preprint. AT: Algebraic Topology papers NAAT: A first textbook on "Non-Abelian Algebraic Topology" QA: Quantum automata and quantum supercomputers NAQAT: Non-Abelian QAT NAAT-List: Category Theory, Homotopy Theory and AT Publications SPE: Stanford Plato: Category Theory and Applications Abc Abstracts1: Springer link Abstracts2: Springer link CERN Preprint Archives: CERN Preprints-1 CERN Articles and Preprint Archives: CERN Preprints-2 QAT1 QAT2 A3
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