Moduli Spaces of Riemannian Metrics / by Wilderich Tuschmann, David J. Wraith.

Format:

Book

Author/Creator:

Tuschmann, Wilderich., Author.

Wraith, David J., Author.

Series:

Oberwolfach Seminars, 1661-237X ; 46

Language:

English

Subjects (All):

Geometry, Differential.

Algebraic topology.

Manifolds (Mathematics).

Complex manifolds.

Differential Geometry.

Algebraic Topology.

Manifolds and Cell Complexes (incl. Diff.Topology).

Local Subjects:

Differential Geometry.

Algebraic Topology.

Manifolds and Cell Complexes (incl. Diff.Topology).

Physical Description:

1 online resource (X, 123 p. 3 illus.)

Edition:

1st ed. 2015.

Place of Publication:

Basel : Springer Basel : Imprint: Birkhäuser, 2015.

Language Note:

English

Summary:

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.

Contents:

Part I: Positive scalar curvature

The (moduli) space of all Riemannian metrics

Clifford algebras and spin

Dirac operators and index theorems

Early results on the space of positive scalar curvature metrics

Kreck-Stolz invariants

Applications of Kreck-Stolz invariants

The eta invariant and applications

The case of dimensions 2 and 3

The observer moduli space and applications

Other topological structures

Negative scalar and Ricci curvature

Part II: Sectional curvature

Moduli spaces of compact manifolds with positive or non-negative sectional curvature

Moduli spaces of compact manifolds with negative and non-positive sectional curvature

Moduli spaces of non-compact manifolds with non-negative sectional curvature

Positive pinching and the Klingenberg-Sakai conjecture.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-0348-0948-4

OCLC:

1066178944