Theorems of Barth-Lefschetz type and Morse Theory on the space of paths in Homogeneous spaces

TL;DR

This paper extends Morse theory-based proofs of homotopy connectedness theorems from Hermitian symmetric spaces to a broader class of compact complex homogeneous spaces, providing new insights into their topological properties.

Contribution

It generalizes Morse theory techniques to a wider class of complex homogeneous spaces, enhancing understanding of their homotopy properties.

Findings

Extended Morse theory proof to more homogeneous spaces

Established homotopy connectedness results for new classes

Provided a unified approach to topological properties

Abstract

Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant proof of homotopy connectedness theorems for complex submanifolds of Hermitian symmetric spaces. In this work we extend this proof to a larger class of compact complex homogeneous spaces.