A Spectral Triple for a Solenoid Based on the Sierpinski Gasket

TL;DR

This paper constructs a spectral triple on a solenoidal space derived from the Sierpinski gasket, exploring its geometric properties through noncommutative geometry techniques.

Contribution

It introduces a novel spectral triple framework for a solenoid based on the Sierpinski gasket, linking fractal geometry with noncommutative geometry.

Findings

Spectral triple captures fractal's geometric features

Analysis of the solenoid's noncommutative geometric structure

Discussion of the spectral triple's main geometrical properties

Abstract

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.