Author: François CharestPublisher: American Mathematical Society
ISBN: 147045310X
Category : Mathematics
Languages : en
Pages : 178
Book Description
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Floer Cohomology and Flips
Author: François CharestPublisher: American Mathematical Society
ISBN: 147045310X
Category : Mathematics
Languages : en
Pages : 178
Book Description
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Symplectic Topology and Floer Homology: Volume 2, Floer Homology and its Applications
Author: Yong-Geun OhPublisher: Cambridge University Press
ISBN: 1316381390
Category : Mathematics
Languages : en
Pages :
Book Description
Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
Symplectic Topology and Floer Homology
Author: Yong-Geun OhPublisher: Cambridge University Press
ISBN: 1107109671
Category : Mathematics
Languages : en
Pages : 471
Book Description
The second part of a two-volume set offering a systematic explanation of symplectic topology. This volume provides a comprehensive introduction to Hamiltonian and Lagrangian Floer theory.
Floer Homology Groups in Yang-Mills Theory
Author: S. K. DonaldsonPublisher: Cambridge University Press
ISBN: 9781139432603
Category : Mathematics
Languages : en
Pages : 254
Book Description
The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
Combinatorial Floer Homology
Author: Vin de SilvaPublisher: American Mathematical Soc.
ISBN: 0821898868
Category : Mathematics
Languages : en
Pages : 114
Book Description
The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
Author: Sebastian Casalaina-MartinPublisher: American Mathematical Society
ISBN: 1470460203
Category : Mathematics
Languages : en
Pages : 112
Book Description
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Twenty-Four Hours of Local Cohomology
Author: Srikanth B. IyengarPublisher: American Mathematical Society
ISBN: 1470471590
Category : Mathematics
Languages : en
Pages : 108
Book Description
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Cornered Heegaard Floer Homology
Author: Christopher L DouglasPublisher: American Mathematical Soc.
ISBN: 1470437716
Category : Education
Languages : en
Pages : 111
Book Description
Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.
Bordered Heegaard Floer Homology
Author: Robert LipshitzPublisher: American Mathematical Soc.
ISBN: 1470428881
Category : Floer homology
Languages : en
Pages : 279
Book Description
The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.
Planar Algebras in Braided Tensor Categories
Author: André Gil HenriquesPublisher: American Mathematical Society
ISBN: 1470455404
Category : Mathematics
Languages : en
Pages : 100
Book Description
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