Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds
Ioannis P. Zois
TL;DR
This paper introduces new invariants for 3-manifolds derived from taut foliations and noncommutative geometry, aiming to extend topological quantum field theories into the noncommutative setting.
Contribution
It proposes novel invariants for 3-manifolds based on taut foliations and noncommutative geometry, advancing the generalization of TQFTs.
Findings
New invariants for 3-manifolds defined
Techniques from noncommutative geometry applied
Potential framework for noncommutative TQFTs
Abstract
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field Theories in the Noncommutative geometry / topology realm.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Geometric and Algebraic Topology · Advanced Operator Algebra Research