Connes-Landi Deformation of Spectral Triples

TL;DR

This paper introduces a method to deform spectral triples using a 2-torus action and a real parameter, preserving their K-theoretic invariants, inspired by Connes-Landi deformation of manifolds.

Contribution

It presents a new deformation technique for spectral triples that maintains K-theoretic invariants, extending Connes-Landi's approach to noncommutative geometry.

Findings

Deformations preserve K-theoretic invariants.

Deformation depends on a real parameter.

Deformations are naturally isomorphic in K-theory.

Abstract

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic $K$-theoretic invariants independent of the deformation parameter.