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- W1593875742 abstract "Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle, f_C : D(T*N) --> C, when f is real analytic. By construction, pi: E --> C comes with an explicit regular fiber M and vanishing spheres V_1,...,V_m in M, one for each critical point of f. Our main result is that (E,pi) is a good model for the complexification (D(T*N),f_C) in the sense that N embeds in E as an exact Lagrangian submanifold, and in addition, pi|N = f and E is homotopy equivalent to N. There are several potential applications in symplectic topology, which we discuss in the introduction." @default.
- W1593875742 created "2016-06-24" @default.
- W1593875742 creator A5033557408 @default.
- W1593875742 date "2009-06-08" @default.
- W1593875742 modified "2023-09-27" @default.
- W1593875742 title "The Picard-Lefschetz theory of complexified Morse functions" @default.
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