Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Taubess_Gromov_invariant> ?p ?o }
Showing triples 1 to 34 of
34
with 100 triples per page.
- Taubess_Gromov_invariant abstract "In mathematics, the Gromov invariant of Clifford Taubes counts embedded (possibly disconnected) pseudoholomorphic curves in a symplectic 4-manifold, where the curves are holomorphic with respect to an auxiliary compatible almost complex structure. (Multiple covers of 2-tori with self-intersection −1 are also counted.)Taubes proved the information contained in this invariant is equivalent to invariants derived from the Seiberg–Witten equations in a series of four long papers. Much of the analytical complexity connected to this invariant comes from properly counting multiply covered pseudoholomorphic curves so that the result is invariant of the choice of almost complex structure. The crux is a topologically defined index for pseudoholomorphic curves which controls embeddedness and bounds the Fredholm index.Embedded contact homology is an extension due to Michael Hutchings of this work to noncompact four-manifolds of the form Y × R, where Y is a compact contact three-manifold. ECH is a symplectic field theory-like invariant; namely, it is the homology of a chain complex generated by certain combinations of Reeb orbits of a contact form on Y, and whose differential counts certain embedded pseudoholomorphic curves and multiply covered pseudoholomorphic cylinders with \"ECH index\" 1 in Y × R. The ECH index is a version of Taubes's index for the cylindrical case, and again, the curves are pseudoholomorphic with respect to a suitable almost complex structure. The result is a topological invariant of Y, which Taubes proved is isomorphic to monopole Floer homology, a version of Seiberg-Witten homology for Y.".
- Taubess_Gromov_invariant wikiPageID "3008788".
- Taubess_Gromov_invariant wikiPageLength "2464".
- Taubess_Gromov_invariant wikiPageOutDegree "15".
- Taubess_Gromov_invariant wikiPageRevisionID "675709601".
- Taubess_Gromov_invariant wikiPageWikiLink 4-manifold.
- Taubess_Gromov_invariant wikiPageWikiLink Almost_complex_manifold.
- Taubess_Gromov_invariant wikiPageWikiLink Category:4-manifolds.
- Taubess_Gromov_invariant wikiPageWikiLink Category:Symplectic_topology.
- Taubess_Gromov_invariant wikiPageWikiLink Clifford_Taubes.
- Taubess_Gromov_invariant wikiPageWikiLink Contact_geometry.
- Taubess_Gromov_invariant wikiPageWikiLink Floer_homology.
- Taubess_Gromov_invariant wikiPageWikiLink Fredholm_operator.
- Taubess_Gromov_invariant wikiPageWikiLink Geometry_&_Topology.
- Taubess_Gromov_invariant wikiPageWikiLink Mathematics.
- Taubess_Gromov_invariant wikiPageWikiLink Pseudoholomorphic_curve.
- Taubess_Gromov_invariant wikiPageWikiLink Reeb_orbit.
- Taubess_Gromov_invariant wikiPageWikiLink Seiberg–Witten_invariant.
- Taubess_Gromov_invariant wikiPageWikiLink Symplectic_field_theory.
- Taubess_Gromov_invariant wikiPageWikiLink Symplectic_geometry.
- Taubess_Gromov_invariant wikiPageWikiLinkText "Taubes's Gromov invariant".
- Taubess_Gromov_invariant wikiPageUsesTemplate Template:Cite_book.
- Taubess_Gromov_invariant wikiPageUsesTemplate Template:Cite_journal.
- Taubess_Gromov_invariant wikiPageUsesTemplate Template:Geometry-stub.
- Taubess_Gromov_invariant subject Category:4-manifolds.
- Taubess_Gromov_invariant subject Category:Symplectic_topology.
- Taubess_Gromov_invariant type Redirect.
- Taubess_Gromov_invariant comment "In mathematics, the Gromov invariant of Clifford Taubes counts embedded (possibly disconnected) pseudoholomorphic curves in a symplectic 4-manifold, where the curves are holomorphic with respect to an auxiliary compatible almost complex structure. (Multiple covers of 2-tori with self-intersection −1 are also counted.)Taubes proved the information contained in this invariant is equivalent to invariants derived from the Seiberg–Witten equations in a series of four long papers.".
- Taubess_Gromov_invariant label "Taubes's Gromov invariant".
- Taubess_Gromov_invariant sameAs Q7688649.
- Taubess_Gromov_invariant sameAs m.08k859.
- Taubess_Gromov_invariant sameAs Q7688649.
- Taubess_Gromov_invariant wasDerivedFrom Taubess_Gromov_invariant?oldid=675709601.
- Taubess_Gromov_invariant isPrimaryTopicOf Taubess_Gromov_invariant.