On Space's Topology

TL;DR

This paper explores the possibility that our universe's space-time might be better modeled as a pseudomanifold with inherent singularities, challenging the traditional manifold assumption in cosmology.

Contribution

It introduces the concept of space-time pseudomanifolds and discusses their topological properties as an alternative to standard manifold models.

Findings

Pseudomanifolds have inherent singularities not removable by topology.

The concept extends naturally to higher dimensions.

Challenges the traditional four-dimensional manifold assumption for space-time.

Abstract

It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even a generalized pseudomanifold of one dimension or another). Basically, a pseudomanifold is in a sense a manifold K with certain irremovable singularities inherited in the topological structure of K, and prior and independent to any metric or differential structure imposed on K. We explain this term for dimension 3, but it holds analogously for higher dimensions as well ([5], [2,Sec.4]).