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## The Maurer–Cartan Form

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0015
- Subject:
- Mathematics, Educational Mathematics

This chapter illustrates the Maurer-Cartan form. On every Lie group G with Lie algebra g, there is a unique canonically defined left-invariant g-valued 1-form called the Maurer-Cartan form. The ... More

## Curvature on a Principal Bundle

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0017
- Subject:
- Mathematics, Educational Mathematics

This chapter examines curvature on a principal bundle. The curvature of a connection on a principal G-bundle is a g-valued 2-form that measures, in some sense, the deviation of the connection from ... More

## The Structure Object

*Ercüment H. Ortaçgil*

### in An Alternative Approach to Lie Groups and Geometric Structures

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198821656
- eISBN:
- 9780191860959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821656.003.0008
- Subject:
- Mathematics, Pure Mathematics

In this chapter, which ends Part I on the fundamental concepts, the theory developed so far is compared with the classical one via the Maurer–Cartan form.

## An Alternative Approach to Lie Groups and Geometric Structures

*Ercüment H. Ortaçgil*

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198821656
- eISBN:
- 9780191860959
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821656.001.0001
- Subject:
- Mathematics, Pure Mathematics

This book is about the foundations of geometric symmetry, namely, Lie groups and differential geometry. Although this is a classical subject about which hundreds of books have been written, this book ... More

## Introduction

*Ercüment H. Ortaçgil*

### in An Alternative Approach to Lie Groups and Geometric Structures

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198821656
- eISBN:
- 9780191860959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821656.003.0001
- Subject:
- Mathematics, Pure Mathematics

This introductory chapter explain the unique feature of this book that makes it different from the classical books on the subject.

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