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- W1999331337 abstract "We show that totally elliptic Lefschetz fibrations that admit a section are classified by their real loci which is nothing but an $S^1$-valued Morse function on the part of the total space. We assign to each such locus a certain combinatorial object that we call a emph{necklace diagram}. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally elliptic Lefschetz fibration that admits a 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 elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally elliptic Lefschetz fibrations which may not have a section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of fibrations." @default.
- W1999331337 created "2016-06-24" @default.
- W1999331337 creator A5024758804 @default.
- W1999331337 date "2011-04-10" @default.
- W1999331337 modified "2023-09-26" @default.
- W1999331337 title "Classification of totally real elliptic Lefschetz fibrations via necklace diagrams" @default.
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