TAUTOLOGICAL RELATIONS AND THE r-SPIN WITTEN CONJECTURE
2010 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, Vol. 43, no 4, 621-658 p.Article in journal (Refereed) Published
In , A Givental introduced a group action on the space of Gromov-Witten potentials and proved its transitivity on the semi-simple potentials In [24, 25], Y-P Lee showed, modulo certain results announced by C Teleman, that this action respects the tautological relations in the cohomology ring of the moduli space (M) over bar (g, n) of stable pointed curves Here we give a simpler proof of this result In particular. it implies that in any semi-simple Gromov-Witten theory where arbitrary correlators can be expressed in genus 0 correlators using only tautological relations, the geometric Gromov-Witten potential coincides with the potential constructed via Givental's group action As the most important application we show that our results suffice to deduce the statement of a 1991 Witten conjecture relating the r-KdV hierarchy to the midsection theory on the space of r-spin structures on stable curves We use the fact that Givental's construction is, in this case, compatible with Witten's conjecture, as Givental himself showed in 
Place, publisher, year, edition, pages
2010. Vol. 43, no 4, 621-658 p.
IdentifiersURN: urn:nbn:se:kth:diva-46642ISI: 000283033400004ScopusID: 2-s2.0-77955339732OAI: oai:DiVA.org:kth-46642DiVA: diva2:455712
FunderSwedish Research Council
QC 201111112011-11-112011-11-042011-11-11Bibliographically approved