2022/07/25 by Ibarra, Dionne
#57K10 (Primary) #57K50 #57R25 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2207.12149
We survey, complete, and modify a proof, involving knot theory, of Stiefel's theorem that all orientable 3-manifolds are parallelizable. The completion of the proof is done by using the relationship between the tangent bundle and normal bundle of manifolds with non-trivial boundary and on stably parallelizable and parallelizable manifolds. We end with a remark on 7-manifolds and present J. Korbaš' example of a non-parallelizable 7-manifold.