Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 020, 21 pages      arXiv:2005.14225      https://doi.org/10.3842/SIGMA.2021.020
Contribution to the Special Issue on Noncommutative Manifolds and their Symmetries in honour of Giovanni Landi

A Spectral Triple for a Solenoid Based on the Sierpinski Gasket

Valeriano Aiello a, Daniele Guido b and Tommaso Isola b
a) Mathematisches Institut, Universität Bern, Alpeneggstrasse 22, 3012 Bern, Switzerland
b) Dipartimento di Matematica, Università di Roma ''Tor Vergata'', I-00133 Roma, Italy

Received June 23, 2020, in final form February 10, 2021; Published online March 02, 2021

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.

Key words: self-similar fractals; noncommutative geometry; ramified coverings.

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