Four-dimensional topology: an introduction

Computational Topology - an Introduction

Four-dimensional CDT with toroidal topology

3 + 1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we show that the system will fluctuate around a dynamically formed background geometry which can be understood from a simple minisuperspace action which conta...

Four Dimensional Quantum Topology Changes of Spacetimes

We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant negative curvature solutions of the Einstein equation i.e. hyperbolic geometries. Using four dimensional polytopes, we can explicitly construct hyperbolic manif...

Introduction to Topology

2 Product topology, Subspace topology, Closed sets, and Limit Points 6 2.1 The Product Topology on X × Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The Subspace Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Closed Sets, Closure, Interior, and limit points . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Sub...

Introduction to Topology