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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Gewicht
ISBN-13
978-0-8218-3724-5 (9780821837245)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Hans U. Boden, McMaster University, Hamilton, ON, Canada,
An involution acting nontrivially on Heegaard-Floer homology by S. Akbulut and S. Durusoy Pseudoholomorphic curves in four-orbifolds and some applications by W. Chen Floer homology for knots and 3-manifolds and cyclic Dehn surgeries along knots by O. Collin A $PSL_2(\mathbb{C})$ Casson invariant by C. L. Curtis The Borel/Novikov conjectures and stable diffeomorphisms of 4-manifolds by J. F. Davis Invariants of knots, embeddings and immersions via contact geometry by T. Ekholm and J. B. Etnyre SO(3)-monopoles: The overlap problem by P. M. N. Feehan and T. G. Leness Heegaard Floer homology of mapping tori II by S. Jabuka and T. Mark Surfaces in 4-manifolds and the surgery conjecture by V. S. Krushkal Symplectic gluing and family Gromov-Witten invariants by J. Lee and T. H. Parker Heegaard splittings and Seiberg-Witten monopoles by Y.-J. Lee Existence of symplectic surfaces by T.-J. Li On the Heegaard Floer homology of $S^3_{-d}(K)$ and unicuspidal rational plane curves by A. Nemethi Examples of symplectic 4-manifolds with positive signature by M. Niepel Definite manifolds bounded by rational homology three spheres by B. Owens and S. Strle On Park's exotic smooth four-manifolds by P. Ozsvath and Z. Szabo Knot polynomials and knot homologies by J. Rasmussen Casson-type invariants in dimension four by D. Ruberman and N. Saveliev Culler-Shalen norms and invariant trace fields by S. Schack and X. Zhang Complex spin structures on 3-manifolds by L. R. Taylor Lefschetz fibrations and pseudoholomorphic curves by M. Usher The isotopy problem for symplectic 4-manifolds by S. Vidussi.
