Track My Order
Help Centre
1300 187 187
Likes
My Wish ListsLogin / Join
Booktopia
Australia's local bookstore
Computers, Rigidity, and Moduli : The Large-Scale Fractal Geometry of Riemannian Moduli Space - Shmuel Weinberger

Computers, Rigidity, and Moduli

The Large-Scale Fractal Geometry of Riemannian Moduli Space

By: Shmuel Weinberger

Hardcover | 28 February 2005

At a Glance

Hardcover

RRP $145.00

$105.50

27%OFF

or 4 interest-free payments of $26.38 with

 or 

Aims to ship in 5 to 10 business days

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 doppelgangers--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.

Industry Reviews
"This is a terrific book. It does no less than introduce an entire new field of mathematics - a truly astounding development. It will be widely read, I think, as much because of the masterful exposition as for the beautiful mathematics. Weinberger gives very clear and accessible descriptions of all the relevant tools from computability, topology, and geometry, in a friendly and engaging style. He has done the mathematical community a great service indeed." - Robin Forman, Rice University; "This book represents a very exciting new area of research at the interface of topology and logic. Written in a quite readable style, and presenting the more accessible cases in detail while giving references for the more involved results, it is a book whose methods and ideas will surely have many more significant applications over the next several years." - Kevin M. Whtye, University of Illinois at Chicago"

You Can Find This Book In

Non-FictionComputing & I.T.Computer ScienceMathematical Theory of ComputationMathematicsGeometryDifferential & Riemannian GeometryAnalytic GeometryMathematical FoundationMathematical LogicTopologyEuclidean Geometry
Fractal Geometry

More in Geometry

Calculus : 3rd Edition - Michael Spivak

Calculus

3rd Edition

Hardcover

RRP $91.95

$79.90

13%
OFF
The Maths Book : Big Ideas Simply Explained - DK

The Maths Book

Big Ideas Simply Explained

Hardcover

RRP $42.99

$32.50

24%
OFF
Topology at Infinity of Discrete Groups - Ross Geoghegan

Topology at Infinity of Discrete Groups

Paperback

RRP $347.00

$312.50

10%
OFF
Geometry, Groups and Mathematical Philosophy - Krishnendu Gongopadhyay

Geometry, Groups and Mathematical Philosophy

Paperback

RRP $347.00

$312.50

10%
OFF
Lectures on Differential Geometry - Bennett Chow

Lectures on Differential Geometry

Hardcover

$376.40

$p$-Adic Hodge Theory for Artin Stacks - Dmitry Kubrak

$p$-Adic Hodge Theory for Artin Stacks

Paperback

RRP $219.00

$197.25

10%
OFF
Drinfeld Modular Forms of Arbitrary Rank - Dirk Basson

Drinfeld Modular Forms of Arbitrary Rank

Paperback

RRP $219.00

$197.25

10%
OFF
Lectures on Differential Geometry - Bennett Chow

Lectures on Differential Geometry

Paperback

RRP $229.00

$206.25

10%
OFF
Group Actions and Equivariant Cohomology - Loring W. Tu

Group Actions and Equivariant Cohomology

Paperback

$376.40

Cataland : Why the Fuss? - Christian Stump

Cataland

Why the Fuss?

Paperback

RRP $219.00

$197.25

10%
OFF
Equivariant Infinite Loop Space Theory : The Space Level Story - J. Peter May

Equivariant Infinite Loop Space Theory

The Space Level Story

Paperback

RRP $219.00

$197.25

10%
OFF
Introduction to Lie Algebras : Finite and Infinite Dimension - J. I. Hall

Introduction to Lie Algebras

Finite and Infinite Dimension

Paperback

RRP $229.00

$206.25

10%
OFF

This product is categorised by