The Seiberg-Witten equations and applications to the topology of smooth four-manifolds /

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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...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Morgan, John, 1946 March 21- (Auteur)
Format: Électronique eBook
Langue:Inglés
Publié: Princeton, New Jersey : Princeton University Press, 1996.
Collection:Mathematical notes (Princeton University Press) ; 44.
Sujets:
Four-manifolds (Topology)
Seiberg-Witten invariants.
Mathematical physics.
Variétés topologiques à 4 dimensions.
Invariants de Seiberg-Witten.
Physique mathématique.
MATHEMATICS > Topology.
Affine space.
Affine transformation.
Algebra bundle.
Algebraic surface.
Almost complex manifold.
Automorphism.
Banach space.
Clifford algebra.
Cohomology.
Cokernel.
Complex dimension.
Complex manifold.
Complex plane.
Complex projective space.
Complex vector bundle.
Complexification (Lie group).
Computation.
Configuration space.
Conjugate transpose.
Covariant derivative.
Curvature form.
Curvature.
Differentiable manifold.
Differential topology.
Dimension (vector space).
Dirac equation.
Dirac operator.
Division algebra.
Donaldson theory.
Duality (mathematics).
Eigenvalues and eigenvectors.
Elliptic operator.
Elliptic surface.
Equation.
Fiber bundle.
Frenet-Serret formulas.
Gauge fixing.
Gauge theory.
Gaussian curvature.
Geometry.
Group homomorphism.
Hilbert space.
Hodge index theorem.
Homology (mathematics).
Homotopy.
Identity (mathematics).
Implicit function theorem.
Intersection form (4-manifold).
Inverse function theorem.
Isomorphism class.
K3 surface.
Kähler manifold.
Levi-Civita connection.
Lie algebra.
Line bundle.
Linear map.
Linear space (geometry).
Linearization.
Manifold.
Mathematical induction.
Moduli space.
Multiplication theorem.
Neighbourhood (mathematics).
One-form.
Open set.
Orientability.
Orthonormal basis.
Parameter space.
Parametric equation.
Parity (mathematics).
Partial derivative.
Principal bundle.
Projection (linear algebra).
Pullback (category theory).
Quadratic form.
Quaternion algebra.
Quotient space (topology).
Riemann surface.
Riemannian manifold.
Sard's theorem.
Sign (mathematics).
Sobolev space.
Spin group.
Spin representation.
Spin structure.
Spinor field.
Subgroup.
Submanifold.
Surjective function.
Symplectic geometry.
Symplectic manifold.
Tangent bundle.
Tangent space.
Tensor product.
Theorem.
Three-dimensional space (mathematics).
Trace (linear algebra).
Transversality (mathematics).
Two-form.
Zariski tangent space.
Accès en ligne:Texto completo
Table des matières:
  • Frontmatter
  • Contents
  • 1. Introduction
  • 2. Clifford Algebras and Spin Groups
  • 3. Spin Bundles and the Dirac Operator
  • 4. The Seiberg-Witten Moduli Space
  • 5. Curvature Identities and Bounds
  • 6. The Seiberg-Witten Invariant
  • 7. Invariants of Kahler Surfaces
  • Bibliography.

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