Connections on Associative Varieties
arXiv:2607.14577
summary
The paper extends the concept of connections from smooth manifolds to associative varieties by using a faithful embedding of manifolds into associative varieties, and demonstrates that geodesics exist in this broader setting.
Abstract
We have embedded the category of smooth real -manifolds faithfully into the category of associative varieties, \cite{S2603}. Many constructions on smooth manifolds can then be generalized to associative varieties. Here we will generalize the well known interpretation of connections on manifolds to connections on associative varieties. This eventually proves the existence of geodesics in an associative variety.
Topics & keywords
#associative varieties#connections#smooth manifolds,geodesics,category theoryassociative varietiesconnectionsgeodesicssmooth manifoldscategory embedding