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Finding disjoint surfaces in 3-manifolds

Abstract:

Let M be a compact connected orientable 3-manifold, with non-empty boundary that contains no 2-spheres. We investigate the existence of two properly embedded disjoint surfaces S_1 and S_2 such that M - (S_1 \cup S_2) is connected. We show that there exist two such surfaces if and only if M is neither a Z_2 homology solid torus nor a Z_2 homology cobordism between two tori. In particular, the exterior of a link with at least 3 components always contain two such surfaces. The proof mainly uses ...

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Publication status:
Published

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Publisher copy:
10.1007/s10711-013-9886-6

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
GEOMETRIAE DEDICATA
Volume:
170
Issue:
1
Pages:
385-401
Publication date:
2012-09-14
DOI:
EISSN:
1572-9168
ISSN:
0046-5755
URN:
uuid:2baf7bb0-0ca6-4119-a0f5-e1f974538d54
Source identifiers:
352666
Local pid:
pubs:352666

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