The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points
| dc.creator | Etingof, Pavel | |
| dc.creator | Henriques, Andre | |
| dc.creator | Kamnitzer, Joel | |
| dc.creator | Rains, Eric | |
| dc.date | 2005-07-25 | |
| dc.date | 2007-05-16 | |
| dc.date.accessioned | 2026-07-07T08:01:45Z | |
| dc.date.available | 2026-07-07T08:01:45Z | |
| dc.description | We compute the Poincare polynomial and the cohomology algebra with rational coefficeints of the manifold M_n of real points of the moduli space of algebraic curves of genus 0 with n labeled points. This cohomology is a quadratic algebra, and we conjecture that it is Koszul. We also compute the 2-local torsion in the cohomology of M_n. As was shown by E. Rains in arXiv:math/0610743 the cohomology of M_n does not have odd torsion, so that the above determines the additive structure of the integral homology and cohomology. Further, we prove that the rational homology operad of M_n is the operad of 2-Gerstenhaber algebras, which is closely related to the Hanlon-Wachs operad of 2-Lie algebras (generated by a ternary bracket). Finally, using Drinfeld's theory of quantization of coboundary Lie quasibialgebras, we show that a large series of representations of the quadratic dual Lie algebra L_n of H^*(M_n,Q) (associated to such quasibialgebras) factors through the the natural projection of L_n to the associated graded Lie algebra of the prounipotent completion of the fundamental group of M_n. This leads us to conjecture that the said projection is an isomorphism, which would imply a formula for lower central series ranks of the fundamental group. On the other hand, we show that the spaces M_n are not formal starting from n=6. | |
| dc.description | 43 pages, 4 figures; This is a revised version, containing more detailed explanations | |
| dc.identifier | https://arxiv.org/abs/math/0507514 | |
| dc.identifier | http://arxiv.org/abs/math/0507514 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129011 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Quantum Algebra | |
| dc.title | The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points | |
| dc.type | text |