dc.contributor.author Salepci, Nermin dc.date.accessioned 2016-10-10T12:36:39Z dc.date.available 2016-10-10T12:36:39Z dc.date.issued 2011 dc.identifier.uri http://publications.mfo.de/handle/mfo/1241 dc.description OWLF 2011 en_US dc.description.abstract We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a $necklace diagram$. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally real elliptic Lefschetz fibration that admits a real section, and on the other hand, it refers to a decomposition of the identity into a product of certain matrices in $PSL(2,Z)$. Using an algorithm to find such decompositions, we obtain an explicit list of necklace diagrams associated with certain classes of totally real elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally real elliptic Lefschetz fibrations which may not have a real section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of real fibrations. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2011,13 dc.title Classification of totally real elliptic Lefschetz fibrations via necklace diagrams en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2011-13 local.scientificprogram OWLF 2011 en_US local.series.id OWP-2011-13
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