Table of Contents

1. Introduction; 2. Examples of aspherical manifolds; 3. First contact – The proper category; 4. How can it be true?; 5. Playing the Novikov game; 6. Equivariant Borel conjecture; 7. Existential problems; 8. Epilogue – A survey of some techniques; References; Index.

Promotional Information

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

About the Author

Shmuel Weinberger is Andrew MacLeish Professor of Mathematics at the University of Chicago. His work is on geometry and topology and their applications. To Weinberger, the only thing cooler than discovering some new geometric result (by any method from any area of mathematics) is discovering a hidden geometric side to the seemingly 'ungeometric'. He has written two other books, one on stratified spaces, and the other on the large-scale structure of spaces of Riemannian metrics using tools from logic. An inaugural Fellow of the American Mathematical Society, he is also a Fellow of the American Academy for the Advancement of Science.