Vector Bundles and Connections: An Introduction
This textbook offers a self-contained introduction to the theory of connections on vector bundles that is accessible to both advanced undergraduate students and graduate students. Constructions and proofs of key results are presented in detail in order to be easily understandable and instructive, and each chapter concludes with a set of interesting exercises.

Standard material about vector bundles is covered in the first chapter, with many examples illustrating the main concepts. Chapter 2 is concerned with the theory of connections on vector bundles, with special attention to the curvature of a connection. The third chapter explores several useful topics not always included in similar texts, such as the computation of the holomorphic tangent and canonical bundles of a Grassmann manifold and the curvature of the tautological and tautological quotient bundles. Finally, Chapter 4 discusses Chern, Pontryagin and Euler classes as an important application of the theory of connections on vector bundles to the theory of characteristic classes.

This book can serve as a text for a one-semester course in differential geometry focused on vector bundles and connections, or as a resource for students pursuing studies in algebraic geometry and mathematical physics. Readers should have a basic understanding of manifolds, differential forms, and cohomology.

1148171834
Vector Bundles and Connections: An Introduction
This textbook offers a self-contained introduction to the theory of connections on vector bundles that is accessible to both advanced undergraduate students and graduate students. Constructions and proofs of key results are presented in detail in order to be easily understandable and instructive, and each chapter concludes with a set of interesting exercises.

Standard material about vector bundles is covered in the first chapter, with many examples illustrating the main concepts. Chapter 2 is concerned with the theory of connections on vector bundles, with special attention to the curvature of a connection. The third chapter explores several useful topics not always included in similar texts, such as the computation of the holomorphic tangent and canonical bundles of a Grassmann manifold and the curvature of the tautological and tautological quotient bundles. Finally, Chapter 4 discusses Chern, Pontryagin and Euler classes as an important application of the theory of connections on vector bundles to the theory of characteristic classes.

This book can serve as a text for a one-semester course in differential geometry focused on vector bundles and connections, or as a resource for students pursuing studies in algebraic geometry and mathematical physics. Readers should have a basic understanding of manifolds, differential forms, and cohomology.

54.99 Pre Order
Vector Bundles and Connections: An Introduction

Vector Bundles and Connections: An Introduction

by Johann Davidov
Vector Bundles and Connections: An Introduction
Add to Wishlist
Vector Bundles and Connections: An Introduction

Vector Bundles and Connections: An Introduction

by Johann Davidov

Overview

This textbook offers a self-contained introduction to the theory of connections on vector bundles that is accessible to both advanced undergraduate students and graduate students. Constructions and proofs of key results are presented in detail in order to be easily understandable and instructive, and each chapter concludes with a set of interesting exercises.

Standard material about vector bundles is covered in the first chapter, with many examples illustrating the main concepts. Chapter 2 is concerned with the theory of connections on vector bundles, with special attention to the curvature of a connection. The third chapter explores several useful topics not always included in similar texts, such as the computation of the holomorphic tangent and canonical bundles of a Grassmann manifold and the curvature of the tautological and tautological quotient bundles. Finally, Chapter 4 discusses Chern, Pontryagin and Euler classes as an important application of the theory of connections on vector bundles to the theory of characteristic classes.

This book can serve as a text for a one-semester course in differential geometry focused on vector bundles and connections, or as a resource for students pursuing studies in algebraic geometry and mathematical physics. Readers should have a basic understanding of manifolds, differential forms, and cohomology.

Product Details

ISBN-13: 9783032074027
Publisher: Springer Nature Switzerland
Publication date: 12/12/2025
Series: Compact Textbooks in Mathematics
Pages: 152
Product dimensions: 6.10(w) x 9.25(h) x 0.00(d)

About the Author

Johann Davidov is Emeritus Professor, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Table of Contents

Vector Bundles.- Connections on Vector Bundles.- Tautological (Universal) Bundles.- Chern, Pontryagin, and Euler Classes.

From the B&N Reads Blog
Page 1 of

Customer Reviews