Self-Similarity in Geometry, Algebra and Arithmetic
Number Theory
2015-06-05 v2 Commutative Algebra
Algebraic Geometry
Abstract
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced. Self-similar objects provide a framework in which, one can unite some results and conjectures in different mathematical frameworks. In some general situations, one can define a well-behaved notion of dimension for self-similar objects. Morphisms between self-similar objects are also defined and a categorical treatment of this concept is provided. We conclude by some philosophical remarks.
Cite
@article{arxiv.1211.4968,
title = {Self-Similarity in Geometry, Algebra and Arithmetic},
author = {Arash Rastegar},
journal= {arXiv preprint arXiv:1211.4968},
year = {2015}
}
Comments
15 pages. arXiv admin note: substantial text overlap with arXiv:math/0404498