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Manifold Constructed from Two Tetrahedron: Figure Eight
Manifold Constructed from Two Tetrahedron: Figure Eight

... A mathematical knot is somewhat different from what one would usually consider a knot, i.e of as a piece of string with free ends. The knots in mathematics are always considered to be closed loops. Formally, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3, considered up to con ...
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QFT on curved spacetimes: axiomatic framework and applications

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Informational axioms for quantum theory

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Topological quantum field theory

A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for work related to topological field theory.In condensed matter physics, topological quantum field theories are the low energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states.
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