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TAUTOLOGICAL RELATIONS AND THE r-SPIN WITTEN CONJECTURE
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-2598-4870
2010 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 43, no 4, 621-658 p.Article in journal (Refereed) Published
Abstract [en]

In [11], 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 [10]

Place, publisher, year, edition, pages
2010. Vol. 43, no 4, 621-658 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-46642ISI: 000283033400004Scopus ID: 2-s2.0-77955339732OAI: oai:DiVA.org:kth-46642DiVA: diva2:455712
Funder
Swedish Research Council
Note
QC 20111111Available from: 2011-11-11 Created: 2011-11-04 Last updated: 2017-12-08Bibliographically approved

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