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$\pi_1$-injective surfaces in graph manifolds (1998)

Rubinstein, J. H. ; Wang, S.

Springer

Commentarii mathematici Helvetici 73 (1998), S. 499-515

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ISSN: 1420-8946

Keywords: Key words. Graph manifold, $\pi_1$-injective surface, separable, simple loop conjecture, k-plane property.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. A criterion is given for an immersed horizontal $\pi_1$ -injective surface in a graph manifold to be separable. Examples are constructed of such surfaces, which are not separable and do not satisfy the k-plane property, for any k. It is shown that the simple loop conjecture holds in graph manifolds and that any graph manifold with boundary has an immersed horizontal surface.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s000140050066

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