The discussion focuses on finding a trivialization of the tangent bundle of the torus S^1*S^1 in R^4. It is established that demonstrating the existence of two nowhere vanishing linearly independent vector fields on the torus is sufficient for this purpose. This approach leverages concepts from differential geometry and topology, specifically related to vector fields and tangent bundles. The problem is rooted in the properties of the torus and its manifold structure.
PREREQUISITESMathematicians, differential geometers, and students studying topology who are interested in the properties of manifolds and vector fields.