Computers, Rigidity, and Moduli

Released on by Shmuel Weinberger
preview-18

  • Computers, Rigidity, and Moduli Book Detail

  • Author : Shmuel Weinberger
  • Release Date : 2005
  • Publisher : Princeton University Press
  • Genre : Computers
  • Pages : 204
  • ISBN 13 : 9780691118895
  • File Size : 24,24 MB
DOWNLOAD BOOK

Computers, Rigidity, and Moduli by Shmuel Weinberger PDF Summary

Book Description: This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.

Disclaimer: www.yourbookbest.com does not own Computers, Rigidity, and Moduli books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Computers, Rigidity, and Moduli

Computers, Rigidity, and Moduli

File Size : 35,35 MB
Total View : 6335 Views
DOWNLOAD

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illust

A Course on Surgery Theory

A Course on Surgery Theory

File Size : 19,19 MB
Total View : 823 Views
DOWNLOAD

An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classificati

A Course on Surgery Theory

A Course on Surgery Theory

File Size : 62,62 MB
Total View : 8362 Views
DOWNLOAD

An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classificati

Manifolds and $K$-Theory

Manifolds and $K$-Theory

File Size : 46,46 MB
Total View : 6713 Views
DOWNLOAD

This volume contains the proceedings of the conference on Manifolds, -Theory, and Related Topics, held from June 23–27, 2014, in Dubrovnik, Croatia. The artic

Geometry and Topology

Geometry and Topology

File Size : 85,85 MB
Total View : 713 Views
DOWNLOAD

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and alge