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Riemannian Topology and Geometric Structures on Manifolds

:	Krzysztof Galicki, Santiago R. Simanca
:	Krzysztof Galicki, Santiago R. Simanca
:	Riemannian Topology and Geometric Structures on Manifolds
:	Birkhäuser Basel
:	9780817647438
:	1
:	CHF 144.90
:

:	Geometrie
:	English

:	290
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer's 65^th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.

	Preface	8
	Charles P. Boyer — An Autobiographical Sketch	10
	Charles P. Boyer’s List of Publications	10
	Accepted for Publication	15
	Contents	16
	L2-Cohomology of Spaces with Nonisolated Conical Singularities and Nonmultiplicativity of the Signature	17
	1 Introduction	17
	2 Reviewof L2-Cohomology	23
	3 L2-Cohomology of Generalized Thom Spaces	25
	4 Spectral Sequences	28
	5 The Generalized Thom Isomorphism	29
	6 L2-Signatures of Generalized Thom Spaces	34
	7 L2-Cohomology of Hyperkähler Manifolds	38
	References	39
	Hirzebruch Surfaces and Weighted Projective Planes	41
	1 The Bochner-Flat Metric of Weighted Projective Spaces	42
	2 Calabi Extremal Kähler Metrics on Hirzebruch Surfaces	46
	3 Hirzebruch Surfaces as Toric Kähler Manifolds	52
	4 TheWeighted 2-Plane P2k as a Blow- Down of Fk	59
	References	63
	Quaternionic Kähler Moduli Spaces	65
	1 Introduction	65
	2 Special Kähler Manifolds	66
	3 The Hyperkähler Manifold	67
	4 The Heisenberg Group	70
	5 Quaternionic Structures	71
	6 Taking the Quotient	73
	7 Properties of the Metric	76
	References	77
	Homological Mirror Symmetry and Algebraic Cycles	79
	1 Introduction	79
	2 Definitions	80
	3 The Construction	83
	4 Birational Transformations, Earthquakes, and HMS	86
	5 Homological Mirror Symmetry and Tropical Hodge Conjecture	102
	References	107
	Positive Sasakian Structures on 5-Manifolds	109
	1 Reduction to Algebraic Geometry	114
	2 The Exceptional Cases	118
	3 The Main Series	124
	4 Klt1 Conditions	130
	References	132
	Four-Manifolds, Curvature Bounds, and Convex Geometry	135
	1 Introduction	135
	2 Rudiments of 4-Dimensional Geometry	137
	3 The Seiberg–Witten Equations	142
	4 Monopoles and Convex Hulls	152
	5 Theory and Practice	159
	References	167
	The 1-Nullity of Sasakian Manifolds	169
	1 Introduction	169
	2 Preliminaries	169
	3 The k-Nullity Distribution	170
	4 The 1-Nullity of Sasakian Manifolds	172
	References	175
	New Results in Sasaki–Einstein Geometry	177
	1 Introduction	177
	2 Sasakian Geometry	179
	3 Explicit Constructions of Sasaki–Einstein Manifolds	181
	4 Toric Sasakian Geometry	183
	5 A Variational Problem for the Reeb Vector Field	187
	6 Obstructions to the Existence of Sasaki–Einstein Metrics	193
	References	199
	Some Examples of Toric Sasaki–Einstein Manifolds	201
	1 Introduction	201
	2 Sasakian Manifolds	203
	3 Toric Geometry	205
	4 Einstein Equation	223
	5 Three-Sasakian Manifolds	226
	6 Sasakian Submanifolds	236
	7 Positive Ricci Curvature Examples	243
	8 Higher Dimensional Examples	245
	References	247
	On the Geometry of Cohomogeneity One Manifolds with Positive Curvature	249
	1 Preliminaries	250
	2 Known Examples of Cohomogeneity One Manifolds with Positive Curvature	252
	3 Classification of Cohomogeneity One Manifolds with Positive Curvature	264
	4 Candidates and Hitchin Metrics	269
	References	276
	The Sasaki Cone and Extremal Sasakian Metrics	279
	1 Introduction	279
	2 Preliminaries on Sasakian Geometry	281
	3 The Energy Functional in the Sasaki Cone	285
	4 The Euler–Lagrange Equation for Strongly Extremal Reeb Vector Fields	286
	5 Sasakian Geometry of Links of Isolated Hypersurface Singularities	289
	6 Extremal Sasakian Metrics in Dimension Five	294
	7 Appendix	300
	References	304