
Abstract

1

Introduction

2

Classical Gravity in 2+1
Dimensions


2.1

Why (2+ 1)dimensional gravity is
simple


2.2

Geometric structures


2.3

The ChernSimons formulation


2.4

The ADM approach


2.5

Exact discrete approaches


2.6

Large diffeomorphisms


2.7

The torus universe


2.8

Dynamics

3

Quantum Gravity in 2+1
Dimensions


3.1

Reduced phase space
quantization


3.2

ChernSimons quantization


3.3

Covariant canonical
quantization


3.4

A digression: Observables and the
problem of time


3.5

“Quantum geometry”


3.6

Lattice methods I: PonzanoRegge
and spin foams


3.7

Lattice methods II: Dynamical
triangulations


3.8

Other lattice approaches


3.9

The WheelerDeWitt equation


3.10

Lorentzian path integrals


3.11

Euclidean path integrals and
quantum cosmology

4

What Have We Learned?

5

What Can We Still Learn?

6

Acknowledgments


References


Figures
