The genus of an abstract intersection sequence

Percell, Peter

doi:10.1090/S0002-9939-1976-0405454-9

The genus of an abstract intersection sequence
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Proc. Amer. Math. Soc. 55 (1976), 217-220 Request permission

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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