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An invariant for stallings manifolds from a TQFT
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Resumo(s)
We will present our construction of a class of effectively calculable, isomorphism invariants for Stallings [1] manifolds by constructing a class of Topological Quantum Field Theories (TQFT's) [2] for these manifolds. Given a $2$-dimensional oriented manifold without boundary, $S$, and
an orientation-preserving automorphism $\varphi :S\rightarrow S$, the self-gluing of the cylinder $S\times I$, where $I$ is the standard closed unit interval, is a $3$-dimensional manifold $S_{\varphi }:=\frac{S\times I}{\sim _{\varphi }}$ known as a Stallings manifold, where $\sim _{\varphi }$ is the relation generated by the relation
$\left(x,0\right) \sim \left( \varphi (x),1\right)$. A fundamental feature of TQFT is the gluing together of two spaces along one or more boundary components. Our TQFT approach [3,4] (in [4] this approach was applied in the geometric context of gerbes) describes equally well the self-gluing of a
single space.
Descrição
Palavras-chave
TQFT's Categories Stallings Manifolds
Contexto Educativo
Citação
An Invariant for Stallings Manifolds from a TQFT, Vol. Abstracts - Topology, ICM, 2006.