Bøger i Chicago Lectures in Mathematics Series CLM serien

An edition of the notes written by J. Frank Adams for his lecture series at the University of Chicago in 1967, 1970, and 1971. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology.

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. This title addresses the course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. It covers topics that are useful for algebraic topologists.

Provides a treatment of algebraic topology that reflects the enormous internal developments within the field and retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented.

The principles of symmetry and self-symmetry are expressed in fractals, the subject of study in dimension theory. This book introduces an area of research which has recently appeared in the interface between dimension theory and the theory of dynamical systems, focusing on invariant fractals.

The theorems of Marina Ratner have guided key advances in understanding dynamical systems. Here, the author offers an introduction to these theorems and an account of the proof of Ratner's measure classification theorem. This is a collection of lecture notes aimed at graduate students and brings these theorems to a broader mathematical readership.

This study presents the results of the authors' development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms.