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Riemannian Topology and Geometric Structures on Manifolds

  • Book
  • © 2009

Overview

Editors:
  1. Krzysztof Galicki

    1. Department of Mathematics, University of New Mexico, Albuquerque

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  2. Santiago R. Simanca

    1. Department of Mathematics, University of New Mexico, Albuquerque

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  • Focuses on fundamental ideas and recent advances
  • Includes and discusses open problems in Riemannian topology and related areas
  • Contains original survey articles by distinguished researchers

Part of the book series: Progress in Mathematics (PM, volume 271)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvii
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  2. L 2-Cohomology of Spaces with Nonisolated Conical Singularities and Nonmultiplicativity of the Signature

    • Jeff Cheeger, Xianzhe Dai
    Pages 1-24

  3. Hirzebruch Surfaces and Weighted Projective Planes

    • Paul Gauduchon
    Pages 25-48

  4. Quaternionic Kähler Moduli Spaces

    • Nigel Hitchin
    Pages 49-61

  5. Homological Mirror Symmetry and Algebraic Cycles

    • Ludmil Katzarkov
    Pages 63-92

  6. Positive Sasakian Structures on 5-Manifolds

    • János Kollár
    Pages 93-117

  7. Four-Manifolds, Curvature Bounds, and Convex Geometry

    • Claude LeBrun
    Pages 119-152

  8. The 1-Nullity of Sasakian Manifolds

    • Philippe Rukimbira
    Pages 153-159

  9. New Results in Sasaki—Einstein Geometry

    • James Sparks
    Pages 161-184

  10. Some Examples of Toric Sasaki—Einstein Manifolds

    • Craig van Coevering
    Pages 185-232

  11. On the Geometry of Cohomogeneity One Manifolds with Positive Curvature

    • Wolfgang Ziller
    Pages 233-262

  12. The Sasaki Cone and Extremal Sasakian Metrics

    • Charles P. Boyer, Krzysztof Galicki, Santiago R. Simanca
    Pages 263-290
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About this book

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasaki geometry, and their interrelation to mathematical physics, notably M and superstring theory. Focusing on these fundamental ideas, this collection presents articles with original results, and plausible problems of interest for future research.

Contributors: C.P. Boyer, J. Cheeger, X. Dai, K. Galicki, P. Gauduchon, N. Hitchin, L. Katzarkov, J. Kollár, C. LeBrun, P. Rukimbira, S.R. Simanca, J. Sparks, C. van Coevering, and W. Ziller.

Editors and Affiliations

  • Department of Mathematics, University of New Mexico, Albuquerque

    Krzysztof Galicki, Santiago R. Simanca

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