ON THE STABLE CLASSIFICATION OF FOUR DIMENSIONAL TOPOLOGICAL MANIFOLDS

Date

2024-1-18

Author

Koşar, Uğur Alp

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For some 4-manifolds, lack of a smooth structure forces us to work on microbundles, where their complexity is reduced with working on stable normal bundle and certain lifts of bundle maps to fibrations. Stability generated by connected sums makes classification theorems analogous to that of higher dimensions work, enabling us to compute bordism groups for B-structures. Together with that, for same values of quadratic 2-type, Stiefel-Whitney class, and the Euler characteristic, we can give isomorphism results, for manifolds with chosen fundamental groups.

Subject Keywords

Four dimensional manifolds, Bordism group, Stable classification, Microbundle, Classifying space

URI

https://hdl.handle.net/11511/108353

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Graduate School of Natural and Applied Sciences, Thesis