The research aims to investigate the relationship between compact connected Lie groups with isomorphic higher homotopy groups and their local isomorphism.
Analysis of the structure of compact connected Lie groups
Comparison of higher homotopy groups
Mathematical proofs of local isomorphism properties
Identified that compact connected Lie groups with isomorphic higher homotopy groups are locally isomorphic
Confirmed that this property holds across various examples of Lie groups
Abstract
Compact connected Lie groups with isomorphic higher homotopy groups are locally isomorphic.