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This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortaçgil instead questions the foundations of the subject, and proposes a new direction.
Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.
List of contents
- Fundemental concepts
- 1: Parallelizable manifolds
- 2: The nonlinear curvature
- 3: Local Lie Groups (LLG.s)
- 4: The centralizer
- 5: s-invariance
- 6: The linear curvature
- 7: The structure object
- Some Consequences
- 8: The nonlinear Spencer sequence
- 9: Deformations
- 10: The de Rham cohomology of a LLG
- 11: The linear Spencer sequence
- 12: The secondary characteristic classes
- 13: The homogeneous flow
- 14: The Van Est Theorem
- 15: The symmetry group
- How to Generalize
- 16: Klein geometries
- 17: The universal jet groupoids
- 18: Embeddings of Klein geometries into universal jet groupoids
- 19: The de.nition of a prehomogeneous geometry (PHG)
- 20: Curvature and generalized PHG.s
About the author
Professor Ercüment Ortaçgil received his PhD from Johns Hopkins University in 1985, and then returned home to Turkey to join the mathematics department at Bogazici University, Istanbul. He retired in 2011, and set his mind to the writing this book to inspire further research on the seemingly elementary problems that have enamoured him throughout his career.
Summary
The theory of Lie groups is one of the most important mathematical themes of the last century and belongs to the centre of modern differential geometry. Whilst the subject is well established, this book aims to be the first to approach geometric theory of Lie groups from a new perspective.
Additional text
In this very nice and unusual book, the author proposes an alternative approach to the theory of Lie groups, together with some applications and generalization of it. The approach proposed is inspired by the geometric theory of partial differential equations (PDEs) and Lie pseudogroups. In this respect, it is much closer in spirit to the original works of Lie and Klein than the current modern theory...The book is suitable for students at a master's level.
Report
In this very nice and unusual book, the author proposes an alternative approach to the theory of Lie groups, together with some applications and generalization of it. The approach proposed is inspired by the geometric theory of partial differential equations (PDEs) and Lie pseudogroups. In this respect, it is much closer in spirit to the original works of Lie and Klein than the current modern theory...The book is suitable for students at a master's level. Luca Vitagliano, American Mathematical Society
