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Geometry and Topology of Manifolds
Edited by: Hans U. Boden, Ian Hambleton, and Andrew J. Nicas, McMaster University, Hamilton, ON, Canada, and B. Doug Park, University of Waterloo, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2005; 347 pp; hardcover
Volume: 47
ISBN-10: 0-8218-3724-9
ISBN-13: 978-0-8218-3724-5
List Price: US$120
Member Price: US$96
Order Code: FIC/47
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This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory, Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the many excellent talks delivered at the conference.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in geometric topology.

Table of Contents

  • S. Akbulut and S. Durusoy -- An involution acting nontrivially on Heegaard-Floer homology
  • W. Chen -- Pseudoholomorphic curves in four-orbifolds and some applications
  • O. Collin -- Floer homology for knots and 3-manifolds and cyclic Dehn surgeries along knots
  • C. L. Curtis -- A \(PSL_2(\mathbb{C})\) Casson invariant
  • J. F. Davis -- The Borel/Novikov conjectures and stable diffeomorphisms of 4-manifolds
  • T. Ekholm and J. B. Etnyre -- Invariants of knots, embeddings and immersions via contact geometry
  • P. M. N. Feehan and T. G. Leness -- SO(3)-monopoles: The overlap problem
  • S. Jabuka and T. Mark -- Heegaard Floer homology of mapping tori II
  • V. S. Krushkal -- Surfaces in 4-manifolds and the surgery conjecture
  • J. Lee and T. H. Parker -- Symplectic gluing and family Gromov-Witten invariants
  • Y.-J. Lee -- Heegaard splittings and Seiberg-Witten monopoles
  • T.-J. Li -- Existence of symplectic surfaces
  • A. Némethi -- On the Heegaard Floer homology of \(S^3_{-d}(K)\) and unicuspidal rational plane curves
  • M. Niepel -- Examples of symplectic 4-manifolds with positive signature
  • B. Owens and S. Strle -- Definite manifolds bounded by rational homology three spheres
  • P. Ozsváth and Z. Szabó -- On Park's exotic smooth four-manifolds
  • J. Rasmussen -- Knot polynomials and knot homologies
  • D. Ruberman and N. Saveliev -- Casson-type invariants in dimension four
  • S. Schack and X. Zhang -- Culler-Shalen norms and invariant trace fields
  • L. R. Taylor -- Complex spin structures on 3-manifolds
  • M. Usher -- Lefschetz fibrations and pseudoholomorphic curves
  • S. Vidussi -- The isotopy problem for symplectic 4-manifolds
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