Contact and Symplectic Geometry: Research Articles and Expository Papers from the Newton Institute Programme by C. B. Th

Introduction

Dive into the intricate world of modern geometry with Contact and Symplectic Geometry, a meticulously curated volume edited by C. B. Thomas. Published by Cambridge University Press, this hardcover edition brings together some of the most influential lectures and research papers presented during the special programme at the Isaac Newton Institute in 1994. Designed for advanced students and researchers, the book offers a comprehensive gateway to the rapidly evolving field of symplectic methods—a cornerstone of contemporary mathematics. Whether you are exploring geometric structures for the first time or deepening your expertise, this volume serves as an essential reference that bridges foundational concepts with cutting-edge developments.

Book Overview

Structured in two distinct parts, Contact and Symplectic Geometry begins with an accessible introductory overview that sets the stage for the deeper explorations that follow. The first part features substantial expository articles that explain key ideas with clarity, while the second part presents original research papers that push the boundaries of current knowledge. Many of the results included in this volume appear in print for the first time, offering readers a rare glimpse into the forefront of geometric research. The book covers a wide spectrum of topics, from the fundamentals of symplectic manifolds and contact structures to advanced applications in topology, dynamics, and mathematical physics. This balanced approach makes it an invaluable resource for both learning and reference.

Key Highlights

• Pioneering Content: Contains previously unpublished research results that have shaped the direction of symplectic geometry.
• Expert Contributors: Features lectures and papers from leading mathematicians who participated in the Newton Institute programme.
• Dual Structure: Combines expository articles for foundational understanding with research papers for advanced insights.
• Comprehensive Coverage: Addresses contact geometry, symplectic topology, Hamiltonian dynamics, and their interconnections.
• Authoritative Publisher: Cambridge University Press ensures rigorous academic standards and lasting value.

Inside the Book

The volume opens with a carefully written introduction that orients readers to the landscape of contact and symplectic geometry, explaining key motivations and historical context. Part I consists of several expository chapters that delve into topics such as symplectic embeddings, contact structures on 3-manifolds, and the geometry of moment maps. These chapters are designed to be self-contained, making them ideal for graduate students and researchers transitioning into the field. Part II presents cutting-edge research that explores new invariants, classification results, and connections to other branches of mathematics. Each chapter is supported by clear notation, illustrative examples, and extensive references, ensuring that readers can follow the arguments and explore further on their own.

Key Topics

• Symplectic Manifolds: Foundations, examples, and the role of symplectic forms in geometry and physics.
• Contact Structures: Definitions, classifications, and applications to low-dimensional topology.
• Hamiltonian Dynamics: The interplay between symplectic geometry and classical mechanics.
• Moment Maps and Reductions: Symplectic reduction and its implications for integrable systems.
• Invariants and Obstructions: New invariants for contact and symplectic structures, including recent advances.

Reader Benefits

This book offers a unique opportunity to engage with high-level mathematics in a structured yet exploratory manner. Readers will benefit from the clarity of the expository sections, which break down complex ideas into digestible parts, while the research papers inspire further investigation. The hardcover format ensures durability for repeated use in libraries, study rooms, and research desks. By presenting both foundational and frontier material, the volume helps readers build a solid grounding while staying abreast of contemporary developments. For Indian students and academics, this book serves as a direct link to the global mathematical community, providing insights that are rarely available in standard textbooks.

Learning Outcomes

• Develop a deep understanding of symplectic and contact manifolds, their properties, and their geometric significance.
• Gain familiarity with advanced techniques such as symplectic reduction, contact homology, and Floer theory.
• Learn to apply geometric methods to problems in topology, dynamics, and mathematical physics.
• Acquire the ability to read and critique contemporary research papers in the field.
• Build a conceptual framework for pursuing independent research in symplectic geometry.

Who Should Read

Contact and Symplectic Geometry is ideal for graduate students in mathematics who have completed introductory courses in differential geometry and topology. It is equally valuable for researchers in geometry, topology, and mathematical physics who wish to explore the latest developments in symplectic methods. The book is also suitable for advanced undergraduate students with a strong background in manifold theory who are ready for a challenge. Indian readers preparing for competitive exams or pursuing doctoral studies will find this volume a rich source of advanced material. Additionally, physicists working in Hamiltonian mechanics or geometric quantization will appreciate the mathematical rigor and clarity.

About the Author

C. B. Thomas is a distinguished mathematician known for his contributions to geometry and topology. With a career spanning decades, he has edited and authored numerous works that have influenced the field. His expertise in symplectic and contact geometry is reflected in the careful selection and organization of the papers in this volume. Thomas’s editorial vision ensures that the book is both cohesive and comprehensive, making complex ideas accessible to a wide audience.

About the Publisher

Cambridge University Press is one of the world’s oldest and most respected academic publishers. With a legacy of excellence in mathematics and science, Cambridge delivers authoritative texts that meet the highest scholarly standards. This hardcover edition is a testament to their commitment to producing durable, well-designed books that serve the academic community for generations. For Indian readers, Cambridge titles are synonymous with quality and reliability in mathematical literature.

Conclusion

Contact and Symplectic Geometry is more than a conference proceedings—it is a landmark volume that captures the spirit of mathematical discovery at a pivotal moment. With its blend of exposition and original research, it offers a rare opportunity to learn from the pioneers of the field. Whether you are a student seeking depth or a researcher chasing new ideas, this book deserves a place on your shelf. Order your copy from Bookshops.in today and add a classic to your mathematics library.