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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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