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Monopoles and Three-Manifolds
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  • Cited by 67
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Taubes, Clifford Henry 2007. The Seiberg–Witten equations and the Weinstein conjecture. Geometry & Topology, Vol. 11, Issue. 4, p. 2117.

    Salamon, Dietmar and Wehrheim, Katrin 2008. Instanton Floer homology with Lagrangian boundary conditions. Geometry & Topology, Vol. 12, Issue. 2, p. 747.

    Hutchings, Michael 2008. Floer homology of families I. Algebraic & Geometric Topology, Vol. 8, Issue. 1, p. 435.

    Kim, Hee Jung and Ruberman, Daniel 2008. Smooth surfaces with non-simply-connected complements. Algebraic & Geometric Topology, Vol. 8, Issue. 4, p. 2263.

    Jabuka, Stanislav and Mark, Thomas E 2008. Product formulae for Ozsváth–Szabó 4–manifold invariants. Geometry & Topology, Vol. 12, Issue. 3, p. 1557.

    Cotton-Clay, Andrew 2009. Symplectic Floer homology of area-preserving surface diffeomorphisms. Geometry & Topology, Vol. 13, Issue. 5, p. 2619.

    Hutchings, Michael and Taubes, Clifford Henry 2009. The Weinstein conjecture for stable Hamiltonian structures. Geometry & Topology, Vol. 13, Issue. 2, p. 901.

    Gay, David T and Stipsicz, András I 2009. Symplectic surgeries and normal surface singularities. Algebraic & Geometric Topology, Vol. 9, Issue. 4, p. 2203.

    Kutluhan, Çağatay and Taubes, Clifford Henry 2009. Seiberg–Witten Floer homology and symplectic forms on S1× M3. Geometry & Topology, Vol. 13, Issue. 1, p. 493.

    Taubes, Clifford Henry 2009. The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field. Geometry & Topology, Vol. 13, Issue. 3, p. 1337.

    Taubes, Clifford Henry 2010. Embedded contact homology and Seiberg–Witten Floer cohomology I. Geometry & Topology, Vol. 14, Issue. 5, p. 2497.

    Ai, Yinghua and Peters, Thomas D 2010. The twisted Floer homology of torus bundles. Algebraic & Geometric Topology, Vol. 10, Issue. 2, p. 679.

    Taubes, Clifford Henry 2010. Embedded contact homology and Seiberg–Witten Floer cohomology IV. Geometry & Topology, Vol. 14, Issue. 5, p. 2819.

    Taubes, Clifford Henry 2010. Embedded contact homology and Seiberg–Witten Floer cohomology V. Geometry & Topology, Vol. 14, Issue. 5, p. 2961.

    Taubes, Clifford Henry 2010. Embedded contact homology and Seiberg–Witten Floer cohomology III. Geometry & Topology, Vol. 14, Issue. 5, p. 2721.

    Kronheimer, Peter and Mrowka, Tomasz 2010. Instanton Floer homology and the Alexander polynomial. Algebraic & Geometric Topology, Vol. 10, Issue. 3, p. 1715.

    Taubes, Clifford Henry 2010. Embedded contact homology and Seiberg–Witten Floer cohomology II. Geometry & Topology, Vol. 14, Issue. 5, p. 2583.

    Bloom, Jonathan M. 2011. A link surgery spectral sequence in monopole Floer homology. Advances in Mathematics, Vol. 226, Issue. 4, p. 3216.

    Golovko, Roman 2011. The embedded contact homology of sutured solid tori. Algebraic & Geometric Topology, Vol. 11, Issue. 2, p. 1001.

    Colin, Vincent Ghiggini, Paolo Honda, Ko and Hutchings, Michael 2011. Sutures and contact homology I. Geometry & Topology, Vol. 15, Issue. 3, p. 1749.

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    Monopoles and Three-Manifolds
    • Online ISBN: 9780511543111
    • Book DOI: https://doi.org/10.1017/CBO9780511543111
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Book description

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg–Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides a full discussion of a central part of the study of the topology of manifolds.

Reviews

'… there are mathematics books that are classics; these are books that tell a particular story in the right way. As such, they will never go out of date and never be bettered. Kronheimer and Mrowka's book is almost surely such a book. If you want to learn about Floer homology in the Seiberg–Witten context, you will do no better than to read Kronheimer and Mrowka's masterpiece Monopoles and Three-Manifolds.'

Clifford Henry Taubes Source: Bulletin of the American Mathematical Society

'This long-awaited book is a complete and detailed exposition of the Floer theory for Seiberg-Witten invariants. It is very nicely written and contains all proofs of results. This makes the book an essential tool for both researchers and students working in this area of mathematics.'

Source: Mathematical Reviews

‘This book is the definitive bible for anyone wanting to learn the full story of the various Seiberg-Witten Floer homology theories … There are mathematics books that are classics. As such, they will never go out of date and never be improved. The present masterpiece is almost surely such a book.’

Alexander Felshtyn Source: Zentralblatt MATH

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