Brown's moduli spaces of curves and the gravity operad
| Autor: | Bruno Vallette, Clément Dupont |
|---|---|
| Přispěvatelé: | Max-Planck-Institut für Mathematik ( MPI ), Institut Montpelliérain Alexander Grothendieck ( IMAG ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Jean Alexandre Dieudonné ( JAD ), Université Nice Sophia Antipolis ( UNS ), Université Côte d'Azur ( UCA ) -Université Côte d'Azur ( UCA ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Analyse, Géométrie et Applications ( LAGA ), Université Paris 8 Vincennes-Saint-Denis ( UP8 ) -Université Paris 13 ( UP13 ) -Université Sorbonne Paris Cité ( USPC ) -Institut Galilée-Centre National de la Recherche Scientifique ( CNRS ), Max-Planck-Institut für Mathematik (MPI), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
14H10 Betti number [ MATH.MATH-AT ] Mathematics [math]/Algebraic Topology [math.AT] 01 natural sciences Inversion (discrete mathematics) Mathematics::Algebraic Topology 14C30 Identity (mathematics) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry moduli spaces of genus zero curves Mathematics::K-Theory and Homology 18D50 Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Filtration (mathematics) Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Algebraic number Algebraic Geometry (math.AG) ComputingMilieux_MISCELLANEOUS Mathematics 010102 general mathematics Cohomology [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG] Moduli space operads [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 010307 mathematical physics Geometry and Topology mixed Hodge structures Hodge structure |
| Zdroj: | Geom. Topol. 21, no. 5 (2017), 2811-2850 Geometry and Topology Geometry and Topology, Mathematical Sciences Publishers, 2017, 21 (5), pp.2811-2850. 〈10.2140/gt.2017.21.2811〉 Geometry and Topology, Mathematical Sciences Publishers, 2017, 21 (5), pp.2811-2850. ⟨10.2140/gt.2017.21.2811⟩ Geometry & Topology |
| ISSN: | 1465-3060 1364-0380 |
| Popis: | This paper is built on the following observation: the purity of the mixed Hodge structure on the cohomology of Brown's moduli spaces is essentially equivalent to the freeness of the dihedral operad underlying the gravity operad. We prove these two facts by relying on both the geometric and the algebraic aspects of the problem: the complete geometric description of the cohomology of Brown's moduli spaces and the coradical filtration of cofree cooperads. This gives a conceptual proof of an identity of Bergstr\"om-Brown which expresses the Betti numbers of Brown's moduli spaces via the inversion of a generating series. This also generalizes the Salvatore-Tauraso theorem on the nonsymmetric Lie operad. Comment: 26 pages; corrected Figure 7 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|