We extend Turaev’s theory of Euler structures and torsion invariants on a 3-manifold M to the case of vector fields having generic behavior on ∂M. This allows to easily define gluings of Euler structures and to develop a completely general gluing formula for Reidemeister torsion of 3-manifolds. Lastly, we describe a combinatorial presentation of Euler structures via stream-spines, as a tool to effectively compute torsion.
Borghini, S. (2015). A gluing formula for Reidemeister–Turaev torsion. ANNALI DI MATEMATICA PURA ED APPLICATA, 194(5), 1535-1561 [10.1007/s10231-014-0433-3].
A gluing formula for Reidemeister–Turaev torsion
Borghini, S
2015
Abstract
We extend Turaev’s theory of Euler structures and torsion invariants on a 3-manifold M to the case of vector fields having generic behavior on ∂M. This allows to easily define gluings of Euler structures and to develop a completely general gluing formula for Reidemeister torsion of 3-manifolds. Lastly, we describe a combinatorial presentation of Euler structures via stream-spines, as a tool to effectively compute torsion.
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