Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Connectivity of Cobordisms and Half-Projective TQFT's   We consider a generalization of the axioms of a TQFT, so called
half-projective TQFT's, with an anomaly, $x^{\mu}$, in the composition law.
$\mu$ is a coboundary on the cobordism categories with non-negative, integer
values. The element $x$ of the ring over which the TQFT is defined does not
have to be invertible. In particular, it may be 0. This modification makes it
possible to extend quantum-invariants, which vanish on $S^1\times S^2$, to
non-trivial TQFT's. (A TQFT in the sense of Atiyah with this property has to be
trivial all together). Under a few natural assumptions the notion of a
half-projective TQFT is shown to be the only possible generalization. Based on
separate work with Lyubashenko on connected TQFT's, we construct a large class
of half-projective TQFT's with $x=0$. Their invariants vanish on $S^1\times
S^2$, and they coincide with the Hennings invariant for non-semisimple Hopf
algebras. Several toplogical tools that are relevant for vanishing properties
of such TQFT's are developed. They are concerned with connectivity properties
of cobordisms, as for example maximal non-separating surfaces. We introduce in
particular the notions of ``interior'' homotopy and homology groups, and of
coordinate graphs, which are functions on cobordisms with values in the
morphisms of a graph category. For applications we will prove that
half-projective TQFT's with $x=0$ vanish on cobordisms with infinite interior
homology, and we argue that the order of divergence of the TQFT on a cobordism
in the ``classical limit'' can be estimated by the rank of its maximal free
interior group.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: atom-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: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga