# nLab The Geometry of Physics - An Introduction

Contents

### Context

#### Differential geometry

synthetic differential geometry

Introductions

from point-set topology to differentiable manifolds

Differentials

V-manifolds

smooth space

Tangency

The magic algebraic facts

Theorems

Axiomatics

cohesion

tangent cohesion

differential cohesion

graded differential cohesion

singular cohesion

$\array{ && id &\dashv& id \\ && \vee && \vee \\ &\stackrel{fermionic}{}& \rightrightarrows &\dashv& \rightsquigarrow & \stackrel{bosonic}{} \\ && \bot && \bot \\ &\stackrel{bosonic}{} & \rightsquigarrow &\dashv& \mathrm{R}\!\!\mathrm{h} & \stackrel{rheonomic}{} \\ && \vee && \vee \\ &\stackrel{reduced}{} & \Re &\dashv& \Im & \stackrel{infinitesimal}{} \\ && \bot && \bot \\ &\stackrel{infinitesimal}{}& \Im &\dashv& \& & \stackrel{\text{étale}}{} \\ && \vee && \vee \\ &\stackrel{cohesive}{}& ʃ &\dashv& \flat & \stackrel{discrete}{} \\ && \bot && \bot \\ &\stackrel{discrete}{}& \flat &\dashv& \sharp & \stackrel{continuous}{} \\ && \vee && \vee \\ && \emptyset &\dashv& \ast }$

Models

Lie theory, ∞-Lie theory

differential equations, variational calculus

Chern-Weil theory, ∞-Chern-Weil theory

Cartan geometry (super, higher)

## Surveys, textbooks and lecture notes

This page provides a hyperlinked index for the book

on methods of differential geometry and their meaning and use in physics, especially gravity and gauge theory.

Among the nice aspects of the book are

Related books:

# Contents

## II Geometry and Topology

### 8 The Geometry of Surfaces in $\mathbb{R}^3$

#### 8.5 Gauss’ Theorema Egregium

• theorema egregium?

## II Lie Groups, Bundles and Chern Forms

### Appendix E. Orbits and Morse-Bott Theory in Compact Lie Groups

category: reference

Last revised on October 13, 2020 at 11:43:08. See the history of this page for a list of all contributions to it.