论文标题
横向和框架
Transversality and framed cobordism
论文作者
论文摘要
雷内·汤姆（RenéThom）的横向概念卓著而深远的概念发现了许多强大的应用。最重要的是，它使汤姆能够发展出恢复理论，这使他对光滑歧管的拓扑结构进行了刺耳的洞察力，当时他概括了Lev Lev Pontryagin的早期框架cobordism的概念。对于他的深刻发现，1958年，他被授予了田野勋章。本文为横向理论提供了一种脚踏实地的方法，该方法仅假定有关平滑歧管的基本知识。遵循安德鲁·普特曼（Andrew Putman）的想法，然后使用横向性给出了庞特拉金（Pontryagin of Pontryagin of Pontryagin of Pontryagin of Pontryagin of Goldopy Spheres）的新颖而详细的证明，其原始证明通常被认为很难访问。
René Thom's remarkable and far-reaching concept of transversality has found numerous powerful applications. Most importantly, it allowed Thom to develop cobordism theory, which led to a piercing insight into the topology of smooth manifolds, when he generalized Lev Pontryagin's earlier concept of framed cobordism. For his profound findings, in 1958 he was awarded the Fields Medal. The present paper provides a down-to-earth approach to transversality theory which only assumes basic knowledge about smooth manifolds. Following an idea of Andrew Putman, we then use transversality to give a novel and detailed proof of an isomorphism theorem of Pontryagin about homotopy groups of spheres whose original proof is generally believed to be rather hard to access.
