On The Diffeomorphic Classification Of Highly Connected Manifolds

The diffeomorphic classification of manifolds is one of the core issues in manifold theory.In 1957,Milnor's work on the 7-manifolds broke the understanding that a given topological manifold might possess at most one differentiable structure,which is a milestone.After introducing the work of Milnor,we briefly introduced the classification of highly connected manifolds based on the Milnor's work.Inspired by these results,we solved the classification of highly connected 15-manifolds with the Euler class being zero.In this paper,The first chapter mainly introduces the research background and significance of the classification of differential structure on manifolds,and the structural arrangement of this paper.The second chapter introduces the basic content and basic results of differential manifolds,homology groups and fiber bundles.The first section of the third chapter mainly introduces the diffeomorphic classification of the existing highly connected manifolds.The second section mainly studies the diffeomorphic classification on the 15-dimensional highly connected manifolds.