Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Brown's dihedral moduli space and freedom of the gravity operad
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22017 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 50, no 5, p. 1081-1122Article in journal (Refereed) Published
Abstract [en]

Francis Brown introduced a partial compactification M-0,n(delta) of the moduli space M-0,M-n. We prove that the gravity cooperad, given by the degree-shifted cohomologies of the spaces M-0,M-n, is cofree as a nonsymmetric anticyclic cooperad; moreover, the cogenerators are given by the cohomology groups of M-0,n(delta). As part of the proof we construct an explicit diagrammatically defined basis of H.(M-0,M-n) which is compatible with cooperadic cocomposition, and such that a subset forms a basis of H.(M-0,n(delta)). We show that our results are equivalent to the claim that H-k (M-0,n(delta)) has a pure Hodge structure of weight 2k for all k, and we conclude our paper by giving an independent and completely different proof of this fact. The latter proof uses a new and explicit iterative construction of M-0,n(delta) from A(n-3) by blow-ups and removing divisors, analogous to Kapranov's and Keel's constructions of (M) over bar (0,n) from Pn-3 and (P-1)(n-3), respectively.

Place, publisher, year, edition, pages
2017. Vol. 50, no 5, p. 1081-1122
Keywords [en]
Moduli of curves, mixed Hodge theory, operads, multiple zeta values, Koszul duality for operads
Keywords [fr]
Espaces de modules des courbes, théorie de Hodge mixte, opérades, valeurs zêta multiples, dualité de Koszul des opérades
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-180167DOI: 10.24033/asens.2340ISI: 000417011100001OAI: oai:DiVA.org:su-180167DiVA, id: diva2:1416512
Note

Titel på franska:

Espace de modules dièdre de Brown et liberté de l'opérade de gravité

Available from: 2020-03-24 Created: 2020-03-24 Last updated: 2020-03-24Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textFree full text

Search in DiVA

By author/editor
Alm, Johan
By organisation
Department of Mathematics
In the same journal
Annales Scientifiques de l'Ecole Normale Supérieure
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf