Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds write by Clifford Taubes. This book was released on 2005. Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds available in PDF, EPUB and Kindle. On March 28-30, 1996, International Press, the National Science Foundation, and the University of California sponsored the First Annual International Press Lecture Series, held on the Irvine campus. This volume consists of four papers comprising the proof of the author's result relating the Seiberg-Witten and Gromov invariants of four manifolds.
J-holomorphic Curves and Symplectic Topology
J-holomorphic Curves and Symplectic Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook J-holomorphic Curves and Symplectic Topology write by Dusa McDuff. This book was released on 2012. J-holomorphic Curves and Symplectic Topology available in PDF, EPUB and Kindle. The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.
Seiberg-Witten and Gromov Invariants for Self-dual Harmonic 2-forms
Seiberg-Witten and Gromov Invariants for Self-dual Harmonic 2-forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Seiberg-Witten and Gromov Invariants for Self-dual Harmonic 2-forms write by Chris Gerig. This book was released on 2018. Seiberg-Witten and Gromov Invariants for Self-dual Harmonic 2-forms available in PDF, EPUB and Kindle. For a closed oriented smooth 4-manifold X with $b^2_+(X)>0$, the Seiberg-Witten invariants are well-defined. Taubes' "SW=Gr" theorem asserts that if X carries a symplectic form then these invariants are equal to well-defined counts of pseudoholomorphic curves, Taubes' Gromov invariants. In the absence of a symplectic form there are still nontrivial closed self-dual 2-forms which vanish along a disjoint union of circles and are symplectic elsewhere. This thesis describes well-defined counts of pseudoholomorphic curves in the complement of the zero set of such near-symplectic 2-forms, and it is shown that they recover the Seiberg-Witten invariants (modulo 2). This is an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main results are the following. Given a suitable near-symplectic form w and tubular neighborhood N of its zero set, there are well-defined counts of pseudoholomorphic curves in a completion of the symplectic cobordism (X-N, w) which are asymptotic to certain Reeb orbits on the ends. They can be packaged together to form "near-symplectic" Gromov invariants as a map on the set of spin-c structures of X. They are furthermore equal to the Seiberg-Witten invariants with mod 2 coefficients, where w determines the "chamber" for defining the latter invariants when $b^2_+(X)=1$. In the final chapter, as a non sequitur, a new proof of the Fredholm index formula for punctured pseudoholomorphic curves is sketched. This generalizes Taubes' proof of the Riemann-Roch theorem for compact Riemann surfaces.
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 write by John W. Morgan. This book was released on 2014-09-08. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 available in PDF, EPUB and Kindle. The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
Contact and Symplectic Topology
Contact and Symplectic Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Contact and Symplectic Topology write by Frédéric Bourgeois. This book was released on 2014-03-10. Contact and Symplectic Topology available in PDF, EPUB and Kindle. Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
