Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dualizability in Low-Dimensional Higher Category Theory   These lecture notes form an expanded account of a course given at the Summer
School on Topology and Field Theories held at the Center for Mathematics at the
University of Notre Dame, Indiana during the Summer of 2012. A similar lecture
series was given in Hamburg in January 2013. The lecture notes are divided into
two parts.
  The first part, consisting of the bulk of these notes, provides an expository
account of the author's joint work with Christopher Douglas and Noah Snyder on
dualizability in low-dimensional higher categories and the connection to
low-dimensional topology. The cobordism hypothesis provides bridge between
topology and algebra, establishing important connections between these two
fields. One example of this is the prediction that the $n$-groupoid of
so-called `fully-dualizable' objects in any symmetric monoidal $n$-category
inherits an O(n)-action. However the proof of the cobordism hypothesis outlined
by Lurie is elaborate and inductive. Many consequences of the cobordism
hypothesis, such as the precise form of this O(n)-action, remain mysterious.
The aim of these lectures is to explain how this O(n)-action emerges in a range
of low category numbers ($n \leq 3$).
  The second part of these lecture notes focuses on the author's joint work
with Clark Barwick on the Unicity Theorem, as presented in arXiv:1112.0040.
This theorem and the accompanying machinery provide an axiomatization of the
theory of $(\infty,n)$-categories and several tools for verifying these axioms.
The aim of this portion of the lectures is to provide an introduction to this
material.

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn