Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Picard-Lefschetz theory of complexified Morse functions   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.

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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con