Books in category Mathematics – Topology

Hodge Theory and Complex Algebraic Geometry II:, Volume 2
The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded.

Computers, Rigidity, and Moduli
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic.

Groups of Circle Diffeomorphisms
As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory.

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples.

This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory.

Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book.

This book introduces the reader to linear functional analysis and to related parts of infinitedimensional Banach space theory.

Geometry with an Introduction to Cosmic Topology
Chapters 27 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space.

By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to …

Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized …