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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The genus of an abstract intersection sequence


Author: Peter Percell
Journal: Proc. Amer. Math. Soc. 55 (1976), 217-220
MSC: Primary 57D40
DOI: https://doi.org/10.1090/S0002-9939-1976-0405454-9
MathSciNet review: 0405454
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Abstract: An intersection sequence, denoted $ IS$, is a combinatorial object associated with a normal immersion $ f:{S^1} \to M$ where $ {S^1}$ is an oriented circle and $ M$ is a closed, connected, oriented $ 2$-manifold. The genus of $ IS$, denoted $ \gamma (IS)$, is defined to be the smallest number which is the genus of a manifold $ M$ admitting a realization $ {S^1} \to M$ of $ IS$. A method is given for computing $ \gamma (IS)$ from $ IS$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0405454-9
Keywords: Normal immersion, intersection sequence, realization, genus, tubular neighborhood
Article copyright: © Copyright 1976 American Mathematical Society

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