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- W2473313573 abstract "Classification of Compact 2-manifolds George Winslow It is said that a topologist is a mathematician who can not tell the difference between a doughnut and a coffee cup. The surfaces of the two objects, viewed as topological spaces, are homeomorphic to each other, which is to say that they are topologically equivalent. In this thesis, we acknowledge some of the most well-known examples of surfaces: the sphere, the torus, and the projective plane. We then observe that all surfaces are, in fact, homeomorphic to either the sphere, the torus, a connected sum of tori, a projective plane, or a connected sum of projective planes. Finally, we delve into algebraic topology to determine that the aforementioned surfaces are not homeomorphic to one another, and thus we can place each surface into exactly one of these equivalence classes. Thesis Director: Dr. Marco Aldi Classification of Compact 2-manifolds" @default.
- W2473313573 created "2016-07-22" @default.
- W2473313573 creator A5045409120 @default.
- W2473313573 date "2016-01-01" @default.
- W2473313573 modified "2023-09-23" @default.
- W2473313573 title "Classification of Compact 2-manifolds" @default.
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- W2473313573 doi "https://doi.org/10.25772/5qv6-nb91" @default.
- W2473313573 hasPublicationYear "2016" @default.
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