Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gysin homomorphism for homogeneous spaces via residues - PhD Thesis   The subject of this dissertation is the Gysin homomorphism in equivariant
cohomology for spaces with torus action. We consider spaces which are quotients
of classical semisimple complex linear algebraic groups by a parabolic subgroup
with the natural action of a maximal torus, the so-called partial flag
varieties. We derive formulas for the Gysin homomorphism for the projection to
a point, of the form \[\int_X \alpha = Res_{\mathbf{z}=\infty}
\mathcal{Z}(\mathbf{z}, \mathbf{t}) \cdot \alpha(\mathbf{t}),\] for a certain
residue operation and a map $\mathcal{Z}(\mathbf{z}, \mathbf{t})$, associated
to the root system. The mentioned description relies on two following
generalizations of theorems in symplectic geometry. We adapt to the equivariant
setting (for torus actions) the Jeffrey--Kirwan nonabelian localization and a
theorem relating the cohomology of symplectic reductions by a compact Lie group
and by its maximal torus, following the approach by Martin. Applying the
generalized theorems to certain contractible spaces acted upon by a product of
unitary groups we derive the push-forward formula for partial flag varieties of
types $A$, $B$, $C$ and $D$.

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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex