Classification of certain six manifolds

Date

2023-6-02

Author

Işık, Onur

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Classification of manifolds is a central question in the field of topology. A complete classification for orientable manifolds of dimension greater than or equal to 4 is not possible because of surgery theoretical reasons: any finitely generated group can be realized as the fundamental group of such a manifold and classification of finitely generated groups is theoretically impossible. As a first invariant, one usually fixes the fundamental group. In this thesis, we are interested in classifying certain 6-dimensional orientable man- ifolds. Namely, we study the problem of classifying 6-manifolds with fundamental group isomorphic to Z ⊕ Z and trivial second homotopy group. Following the work of Kreck and Lueck, we show that such manifolds are stably diffeomorphic if and only if they are bordant.

Subject Keywords

Surgery, Homotopy groups, 6-manifolds, Stable diffeomorphism, Bordism

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https://hdl.handle.net/11511/103886

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Graduate School of Natural and Applied Sciences, Thesis