£77.95

Homotopy Equivalences of 3-Manifolds and Deformation Theory of Kleinian Groups (Memoirs of the American Mathematical Society)

Complex Analysis

Price data last checked 10 day(s) ago - will refresh soon

View at Amazon

Price History & Forecast

Last 44 days • 44 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 44 days • 1 price levels

Days at Price

Price Analysis

Most common price: £78 (44 days, 100.0%)

Price range: £78 - £78

Price levels: 1 different prices over 44 days

Description

This text investigates a natural question arising in the topological theory of $3$-manifolds, and applies the results to give new information about the deformation theory of hyperbolic $3$-manifolds. It is well known that some compact $3$-manifolds with boundary admit homotopy equivalences that are not homotopic to homeomorphisms. We investigate when the subgroup $\mathcal{R}(M)$ of outer automorphisms of $\pi_1(M)$ which are induced by homeomorphisms of a compact $3$-manifold $M$ has finite index in the group $\operatorname{Out}(\pi_1(M))$ of all outer automorphisms. This question is completely resolved for Haken $3$-manifolds.It is also resolved for many classes of reducible $3$-manifolds and $3$-manifolds with boundary patterns, including all pared $3$-manifolds. The components of the interior $\operatorname{GF}(\pi_1(M))$ of the space $\operatorname{AH}(\pi_1(M))$ of all (marked) hyperbolic $3$-manifolds homotopy equivalent to $M$ are enumerated by the marked homeomorphism types of manifolds homotopy equivalent to $M$, so one may apply the topological results above to study the topology of this deformation space.We show that $\operatorname{GF}(\pi_1(M))$ has finitely many components if and only if either $M$ has incompressible boundary, but no 'double trouble', or $M$ has compressible boundary and is 'small'. (A hyperbolizable $3$-manifold with incompressible boundary has double trouble if and only if there is a thickened torus component of its characteristic submanifold which intersects the boundary in at least two annuli). More generally, the deformation theory of hyperbolic structures on pared manifolds is analyzed. Some expository sections detail Johannson's formulation of the Jaco-Shalen-Johannson characteristic submanifold theory, the topology of pared $3$-manifolds, and the deformation theory of hyperbolic $3$-manifolds. An epilogue discusses related open problems and recent progress in the deformation theory of hyperbolic $3$-manifolds.

Product Specifications

Format: mass_market
ASIN: 0821835491
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Complex Analysis
Domain: Amazon UK
Release Date: 02 December 2004
Listed Since: 18 December 2006

Barcode

No barcode data available

Homotopy Equivalences of 3-Manifolds and Deformation Theory of Kleinian Groups (Memoirs of the American Mathematical Society)

Price History & Forecast

Price Distribution

Price Analysis

Description

Product Specifications

Barcode

Similar Products You Might Like

Hyperbolic Manifolds and Discrete Groups (Modern Birkhäuser Classics)

The Structure of Classical Diffeomorphism Groups: 400 (Mathematics and Its Applications, 400)

CR Embedded Submanifolds of CR Manifolds (Memoirs of the American Mathematical Society)

Differential Analysis on Complex Manifolds: 65 (Graduate Texts in Mathematics, 65)

Topology and Geometry of Manifolds (Proceedings of Symposia in Pure Mathematics): 2001 Georgia International Topology Conference, May 21-June 2, 2001, University of Georgia, Athens, Georgia

L² Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds (Springer Monographs in Mathematics)

Frobenius Manifolds: Quantum Cohomology and Singularities: 36 (Aspects of Mathematics, 36)

Shapes and Diffeomorphisms: 171 (Applied Mathematical Sciences, 171)

Quasi-projective Moduli for Polarized Manifolds: 30 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 30)

Global Surgery Formula for the Casson-Walker Invariant. (Annals of Mathematics Studies-140)

Extrinsic Geometry of Foliations: 339 (Progress in Mathematics, 339)

Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics): 17

Computers, Rigidity, and Moduli – The Large–Scale Fractal Geometry of Riemannian Moduli Space: 5 (Porter Lectures)

An Introduction to Differential Manifolds

The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)

The Homotopy Category of Simply Connected 4-Manifolds: 297 (London Mathematical Society Lecture Note Series, Series Number 297)

Intersection Homology & Perverse Sheaves: with Applications to Singularities: 281 (Graduate Texts in Mathematics, 281)

Thurston's Work on Surfaces (MN-48) (Mathematical Notes)

The Geometry Of Spherical Space Form Groups (Second Edition): 28 (Series In Pure Mathematics)

Quantum Invariants of Knots and 3-Manifolds (De Gruyter Studies in Mathematics): 18

Extrinsic Geometric Flows: 206 (Graduate Studies in Mathematics)

Equivariant Poincaré Duality on G-Manifolds: Equivariant Gysin Morphism and Equivariant Euler Classes: 2288 (Lecture Notes in Mathematics, 2288)

Topics on Continua (Chapman & Hall/CRC Pure and Applied Mathematics)

Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 2 (Monograph Books)