Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the homotopy type of the space of Sullivan diagrams   We study the homotopy type of the harmonic compactification of the moduli
space of a 2-cobordism S with one outgoing boundary component, or equivalently
of the space of Sullivan diagrams of type S on one circle. Our results are of
two types: vanishing and non-vanishing. In our vanishing results we are able to
show that the connectivity of the harmonic compactification increases with the
number of incoming boundary components. Moreover, we extend the genus
stabilization maps of moduli spaces to the harmonic compactification and show
that the connectivity of these maps increases with the genus and number of
incoming boundary components. In our non-vanishing results we compute the
non-trivial fundamental group of the harmonic compactification of the cobordism
S of any genus with two unenumerated punctures and empty incoming boundary.
Moreover, we construct five infinite families of non-trivial homology classes
of the harmonic compactification, two of which correspond to non-trivial higher
string topology operations.

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The categories of this paper are: q-alg
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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: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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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: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: astro-ph