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57Zxx Relations to quantum topology and physics

This subtopic introduces the core ideas in relations to quantum topology and physics, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

57Z05 Relations of manifolds and cell complexes with physics

Overview

Relations of manifolds and cell complexes with physics. This topic studies interactions between topology and physics, especially quantum invariants and topological structures arising in field theories.

Related Wikipedia Page

Wikipedia: Quantum topology

Useful Links

Key Ideas

  • quantum invariants of manifolds and links
  • topological field-theoretic constructions
  • category-theoretic and representation-theoretic bridges

Typical Uses

Used to transfer techniques between low-dimensional topology, representation theory, and mathematical physics.

Applications

  • Quantum topology
  • TQFT models
  • Knot and 3-manifold invariants

References

Recommended Textbooks