Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lefschetz Theorem Using Real Morse Theory   We prove the Lefschetz hyperplane section theorem using a simpler machinery
by making the observation that we can compose the Lefschetz Pencil with a Real
Morse function to get a map from the variety to $\mathbb{R}$ which is "close"
to being a Real Morse function. The proof uses a new method unlike the
conventional one which uses vanishing cycles, thimbles and monodromy. We prove
the genus formula for plane curves using Morse theory, Lefschetz pencil and
B\'ezout's theorem. And then we prove the Riemann Hurwitz formula for ramified
maps between curves by employing techniques from deformation theory. Lastly, we
prove the Lefschetz Hyperplane Section Theorem solely using Real Morse Theory
and exact sequences.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph