The Mobius Band and the Mobius Foliation
Ioannis P. Zois
TL;DR
This paper introduces a new topological invariant for foliations, computed using noncommutative geometry techniques, motivated by applications in theoretical physics and flat vector bundles.
Contribution
It presents the computation of a novel topological invariant for foliations using noncommutative geometry, expanding the mathematical tools available for studying foliated structures.
Findings
New topological invariant for foliations introduced.
Computed using K-Theory and cyclic cohomology pairing.
Motivated by applications in theoretical physics and flat vector bundles.
Abstract
This article presents some computations for a new topological invariant for foliations introduced some years ago by the author using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology. The motivation came from theoretical physics, more specifically from flat vector bundles, in physics terminology from potentials which are pure gauge.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Geometric and Algebraic Topology