2019/04/03 by Wolfgang Schmaltz, Schmaltz, Wolfgang · 1 citation
Mathematics · Medicine · #53D30 #53D45 #55N32 #57R18 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1904.02186
openalex publication_date 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Steenrod problem for closed orientable manifolds was solved completely by\nThom. Following this approach, we solve the Steenrod problem for closed\norientable orbifolds, proving that the rational homology groups of a closed\norientable orbifold have a basis consisting of classes represented by\nsuborbifolds whose normal bundles have fiberwise trivial isotropy action.\n Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, has yielded a\nwell-defined Gromov-Witten invariant via the regularization of moduli spaces.\nAs an application, we demonstrate that the polyfold Gromov-Witten invariants,\noriginally defined via branched integrals, may equivalently be defined as\nintersection numbers against a basis of representing suborbifolds.\n