Parallelisability of 3-manifolds via surgery
Sebastian Durst, Hansj\"org Geiges, Jes\'us Gonzalo P\'erez, Marc Kegel
TL;DR
This paper proves that all closed, orientable 3-manifolds can be equipped with a parallelisable structure using surgery techniques, enhancing understanding of their geometric properties.
Contribution
It provides two new proofs of parallelisability for all closed, orientable 3-manifolds based on surgery presentations, incorporating contact geometry refinements.
Findings
All closed, orientable 3-manifolds are parallelisable.
Two distinct proofs are provided, one using contact geometry.
The results complement recent work by Benedetti-Lisca.
Abstract
We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish-Wallace surgery presentation; one proof uses a refinement due to Kaplan and some basic contact geometry. This complements a recent paper by Benedetti-Lisca.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics