Dimension, Divergence and Desingularization

TL;DR

This paper discusses the non-uniqueness of geometric descriptions of the universe and proposes using K-theories of algebraic and analytic cycles to achieve a more consistent and unique framework for spacetime and gauge theories.

Contribution

It introduces an abstract K-theoretic approach to spacetime and gauge geometry to address the non-uniqueness in geometric descriptions.

Findings

K-theoretic framework offers potential for unique spacetime descriptions

Highlights limitations of traditional geometric approaches

Proposes a novel algebraic method for gauge-theoretic geometry

Abstract

I argue that consistent geometrical descriptions of the universe are far from unique even as low-energy limits and that an abstract "atomic" description of spacetime and gauge-theoretic geometry in terms of K-theories of algebraic and analytic cycles has the promise to restore uniqueness to our description.