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

Ercüment H. Ortaçgil

Abstract

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 takes a new and innovative approach. The main idea is to replace the Maurer–Cartan form with absolute parallelism and its curvature. Unlike the classical approach, where the model is fixed beforehand by the Maurer–Cartan form, this new approach is model-free, and also revisits the foundational concepts of differential geometry, such as covariant differentiation, from a different perspective.

Keywords: Lie group, geometry, symmetry, Maurer-Cartan form, parallelism, curvature, model free, covariant differentiation

Bibliographic Information

Print publication date: 2018 Print ISBN-13: 9780198821656
Published to Oxford Scholarship Online: September 2018 DOI:10.1093/oso/9780198821656.001.0001

Authors

Affiliations are at time of print publication.

Ercüment H. Ortaçgil, author
Professor Emeritus, Bogazici University