Surgical Methods in Rigidity Tata Institute Lectures on Mathematics and Physics 1st Edition by F Thomas Farrell ISBN 3540589775 9783540589778

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ISBN 10: 3540589775 
ISBN 13: 9783540589778
Author: F Thomas Farrell

The study of rigidity phenomena in geometry and topology has been a central theme in mathematics over the last several decades. Rigidity, broadly speaking, refers to situations where geometric or topological structures are uniquely determined by certain invariants or conditions, allowing very limited or no deformations.

This volume, Surgical Methods in Rigidity, aims to present a comprehensive overview of techniques employing surgery theory to analyze and prove rigidity results. Surgery theory, a powerful tool in geometric topology, provides methods to modify manifolds in controlled ways, enabling classification and understanding of their structures.

In these lectures, I will explore the intricate relationship between algebraic, geometric, and topological aspects of rigidity. The focus will be on how surgical techniques can be applied to resolve problems concerning the classification of manifolds, the behavior of group actions, and the rigidity of large-scale geometric objects.

The content is intended for advanced graduate students and researchers familiar with algebraic topology and differential geometry, but who are new to the interplay between surgery theory and rigidity phenomena. Throughout the course, foundational concepts will be reviewed alongside recent developments, illustrating the depth and breadth of the field.

I hope these lectures serve as a stepping stone toward further exploration and research in this rich and evolving area of mathematics.

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Tags: F Thomas Farrell, Surgical Methods, Rigidity Tata, Mathematics