Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the first Betti number - an approach via Schatten norm
  estimates on semigroup differences   We derive new estimates for the first Betti number of compact Riemannian
manifolds. Our approach relies on the Birman-Schwinger principle and Schatten
norm estimates for semigroup differences. In contrast to previous works we do
not require any a priori ultracontractivity estimates and we provide bounds
which explicitly depend on suitable integral norms of the Ricci tensor.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
29
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: atom-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-th
28
The categories of this paper are: alg-geom