Preprint Article Version 1 This version is not peer-reviewed

Modeling Spacetime as a Branched Covering Space over 2-Knots

Version 1 : Received: 25 July 2019 / Approved: 30 July 2019 / Online: 30 July 2019 (15:09:44 CEST)

How to cite: Duston, C. Modeling Spacetime as a Branched Covering Space over 2-Knots. Preprints 2019, 2019070342 (doi: 10.20944/preprints201907.0342.v1). Duston, C. Modeling Spacetime as a Branched Covering Space over 2-Knots. Preprints 2019, 2019070342 (doi: 10.20944/preprints201907.0342.v1).

Abstract

In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.

Subject Areas

general relativity; geometry; topology; branched covering space; exotic smooth structure; knot theory

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.