Structural properties of bounded one-sided surfaces in link spaces

Details Structural properties of bounded one-sided surfaces in link spaces Structural properties of bounded one-sided surfaces in link spaces

2011-01-13

arxiv.org/abs/1101.2603v1

Mathematics

Geometric Topology

20 pages, 6 figures

Scientific paper

Various structural properties are developed for non-orientable surfaces in link spaces. The M\"obius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights into the change of genus under boundary slope, which are not possible using the existing continued fractions algorithm. A restriction under which geometrically incompressible, boundary compressible one-sided surfaces have a unique boundary incompressible form away from the boundary is established.

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