Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Floer_homology> ?p ?o }
- Floer_homology abstract "In mathematics, Floer homology is a mathematical tool used in the study of symplectic geometry and low-dimensional topology. Floer homology is a novel invariant arising as an infinite-dimensional analog of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called Hamiltonian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as (smooth) three- and four-dimensional manifolds.Floer homology is typically defined by associating to the object of interest an infinite-dimensional manifold and a real valued function on it. In the symplectic version, this is the free loop space of a symplectic manifold with the symplectic action functional. For the (instanton) version for three-manifolds, it is the space of SU(2)-connections on a three-dimensional manifold with the Chern–Simons functional. Loosely speaking, Floer homology is the Morse homology of the function on the infinite-dimensional manifold. A Floer chain complex is formed from the abelian group spanned by the critical points of the function (or possibly certain collections of critical points). The differential of the chain complex is defined by counting the function's gradient flow lines connecting certain pairs of critical points (or collections thereof). Floer homology is the homology of this chain complex.The gradient flow line equation, in a situation where Floer's ideas can be successfully applied, is typically a geometrically meaningful and analytically tractable equation. For symplectic Floer homology, the gradient flow equation for a path in the loopspace is (a perturbed version of) the Cauchy–Riemann equation for a map of a cylinder (the total space of the path of loops) to the symplectic manifold of interest; solutions are known as pseudoholomorphic curves. The Gromov compactness theorem is then used to show that the differential is well-defined and squares to zero, so that the Floer homology is defined. For instanton Floer homology, the gradient flow equations is exactly the Yang-Mills equation on the three-manifold crossed with the real line.".
- Floer_homology wikiPageExternalLink 1104161987.
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- Floer_homology wikiPageExternalLink AtiyahFloer.pdf.
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- Floer_homology wikiPageWikiLink 3-manifold.
- Floer_homology wikiPageWikiLink 4-manifold.
- Floer_homology wikiPageWikiLink Abelian_group.
- Floer_homology wikiPageWikiLink Action_(physics).
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- Floer_homology wikiPageWikiLink Alexander_Givental.
- Floer_homology wikiPageWikiLink Alexander_polynomial.
- Floer_homology wikiPageWikiLink Almost_complex_manifold.
- Floer_homology wikiPageWikiLink Almost_complex_structure.
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- Floer_homology wikiPageWikiLink Arnold_conjecture.
- Floer_homology wikiPageWikiLink Augustin_Banyaga.
- Floer_homology wikiPageWikiLink Betti_number.
- Floer_homology wikiPageWikiLink Birkhäuser.
- Floer_homology wikiPageWikiLink Brane.
- Floer_homology wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
- Floer_homology wikiPageWikiLink Calabi–Yau_manifold.
- Floer_homology wikiPageWikiLink Cambridge_University_Press.
- Floer_homology wikiPageWikiLink Casson_invariant.
- Floer_homology wikiPageWikiLink Categorification.
- Floer_homology wikiPageWikiLink Category:3-manifolds.
- Floer_homology wikiPageWikiLink Category:Gauge_theories.
- Floer_homology wikiPageWikiLink Category:Homology_theory.
- Floer_homology wikiPageWikiLink Category:Mathematical_physics.
- Floer_homology wikiPageWikiLink Category:Morse_theory.
- Floer_homology wikiPageWikiLink Category:Symplectic_topology.
- Floer_homology wikiPageWikiLink Cauchy–Riemann_equation.
- Floer_homology wikiPageWikiLink Cauchy–Riemann_equations.
- Floer_homology wikiPageWikiLink Chain_complex.
- Floer_homology wikiPageWikiLink Chern–Simons.
- Floer_homology wikiPageWikiLink Chern–Simons_theory.
- Floer_homology wikiPageWikiLink Clay_Mathematics_Institute.
- Floer_homology wikiPageWikiLink Clifford_Taubes.
- Floer_homology wikiPageWikiLink Closed_manifold.
- Floer_homology wikiPageWikiLink Cluster_homology.
- Floer_homology wikiPageWikiLink Cobordism.
- Floer_homology wikiPageWikiLink Coherent_sheaf.
- Floer_homology wikiPageWikiLink Coherent_sheaves.
- Floer_homology wikiPageWikiLink Communications_in_Mathematical_Physics.
- Floer_homology wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Floer_homology wikiPageWikiLink Compactification_(mathematics).
- Floer_homology wikiPageWikiLink Connection_(mathematics).
- Floer_homology wikiPageWikiLink Contact_geometry.
- Floer_homology wikiPageWikiLink Contact_manifold.
- Floer_homology wikiPageWikiLink Contact_structure.
- Floer_homology wikiPageWikiLink Cotangent_bundle.
- Floer_homology wikiPageWikiLink Covering_space.
- Floer_homology wikiPageWikiLink Critical_point_(mathematics).
- Floer_homology wikiPageWikiLink Cup_product.
- Floer_homology wikiPageWikiLink Curvature_form.
- Floer_homology wikiPageWikiLink Deck_transformation.
- Floer_homology wikiPageWikiLink Derived_category.
- Floer_homology wikiPageWikiLink Dg_category.
- Floer_homology wikiPageWikiLink Differential.
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- Floer_homology wikiPageWikiLink Donaldson_theory.
- Floer_homology wikiPageWikiLink Double_cover_(topology).
- Floer_homology wikiPageWikiLink Duke_Mathematical_Journal.
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- Floer_homology wikiPageWikiLink Euler_characteristic.
- Floer_homology wikiPageWikiLink Exact_triangle.
- Floer_homology wikiPageWikiLink Ext_functor.
- Floer_homology wikiPageWikiLink Ext_group.
- Floer_homology wikiPageWikiLink Fixed_point_(mathematics).
- Floer_homology wikiPageWikiLink Flat_connection.
- Floer_homology wikiPageWikiLink Flow_line.
- Floer_homology wikiPageWikiLink Flow_lines.
- Floer_homology wikiPageWikiLink Fredholm_index.
- Floer_homology wikiPageWikiLink Fredholm_operator.
- Floer_homology wikiPageWikiLink Free_loop.
- Floer_homology wikiPageWikiLink Free_loop_space.
- Floer_homology wikiPageWikiLink Fukaya_category.
- Floer_homology wikiPageWikiLink Gauge_equivalence.
- Floer_homology wikiPageWikiLink Genus_(mathematics).
- Floer_homology wikiPageWikiLink Geometry_&_Topology.
- Floer_homology wikiPageWikiLink Gradient.
- Floer_homology wikiPageWikiLink Graeme_Segal.
- Floer_homology wikiPageWikiLink Grid_diagrams.
- Floer_homology wikiPageWikiLink Gromov_compactness_theorem.
- Floer_homology wikiPageWikiLink Gromovs_compactness_theorem.
- Floer_homology wikiPageWikiLink Hamiltonian_isotopy.
- Floer_homology wikiPageWikiLink Hamiltonian_symplectomorphism.
- Floer_homology wikiPageWikiLink Heegaard_splitting.
- Floer_homology wikiPageWikiLink Helmut_Hofer.
- Floer_homology wikiPageWikiLink Holomorphic_curve.
- Floer_homology wikiPageWikiLink Homological_mirror_symmetry.
- Floer_homology wikiPageWikiLink Homology_(mathematics).
- Floer_homology wikiPageWikiLink Homology_theories.
- Floer_homology wikiPageWikiLink Instanton.
- Floer_homology wikiPageWikiLink Inventiones_Mathematicae.