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Theorems of Barth-Lefschetz type and Morse theory on the space of paths in homogeneous spaces

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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.

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Acknowledgments

This work is based on the my’s Ph.D. Thesis at Michigan State University. I wish to thank Michigan State University for the support provided during the pursuit of my doctarate. I would like to thank my Advisor Prof Jon Wolfson for suggesting I investigate this topic and for the many helpful discussions.

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  1. Tata Institute of Fundamental Research, Mumbai, India

    Chaitanya Senapathi

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  1. Chaitanya Senapathi
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Correspondence to Chaitanya Senapathi.

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Senapathi, C. Theorems of Barth-Lefschetz type and Morse theory on the space of paths in homogeneous spaces. Geom Dedicata 178, 195–217 (2015). https://doi.org/10.1007/s10711-015-0053-0

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