quantum algebraic topology topics

This is a contributed topics list on quantum algebraic topology.Online resources are also included for selected areas of QAT.

1 Quantum Algebraic Topology (QAT)

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.

1.1 QAT Topics : Online Resources

• QAT:http://planetmath.org/?op=getobj&from=lec&id=68Quantum Algebraic Topology-preprint.

• Axiomatic quantum field theory (AQFT)

• AT:http://www.bangor.ac.uk/ mas010/publicfull.htmAlgebraic Topology papers

• NAAT:http://www.bangor.ac.uk/ mas010/nonab-a-t.htmlA first textbook on “Non-Abelian Algebraic Topology”

• QA:Quantum automata and quantum supercomputers (http://planetmath.org/QuantumAutomataAndQuantumComputation2)

• NAQAT:http://www.bangor.ac.uk/ mas010/pdffiles/BBG-158-NAC0STQG.pdfNon-Abelian QAT

• NAAT-List:http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/07/cathom07.htmlCategory Theory, Homotopy Theory and AT Publications

• SPE:http://plato.stanford.edu/entries/category-theory/Stanford Plato: Category Theory and Applications

• Abc

.2 Additional items

1. QAT1

2. QAT2

3. A3