Topology of 3 Manifolds

Mallick, Sucharita (2022) Topology of 3 Manifolds. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Sucharita Mallick (17MS224)) 17MS224_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

In this project I have introduced vector bundles, fibre bundles and principal Gbundles, various relevant examples has been discussed. In the second chapter the classification theorem of principal G-bundles over a space X, has been discussed. Then I have described a few related groups that are isomorphic to V ect¹(X), the isomorphism classes of line bundles over a space X. Then I go into the main goal of proving Stiefel’s theorem for the case where the manifold is closed. The proof mainly uses Stiefel-Whitney classes and lifting of the classifying map through the Whitehead tower of BO(3).

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