Semião, Paulo2014-06-202014-06-202006An Invariant for Stallings Manifolds from a TQFT, Vol. Abstracts - Topology, ICM, 2006.978-3-03719-022-7AUT: PSE00609;http://hdl.handle.net/10400.1/4448We 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.engTQFT'sCategoriesStallings Manifoldsconference object