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EMBEDDINGS OF 2-COMPLEXES INTO 3-MANIFOLDS

JANINA GLOCK

Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert Mayer Straße 6-10, D-60325 Frankfurt, Germany

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and

CYNTHIA I. HOG-ANGELONI

Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert Mayer Straße 6-10, D-60325 Frankfurt, Germany

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https://doi.org/10.1142/S0218216505003725Cited by:0 (Source: Crossref)

Abstract

Let f: K² → M³ be an embedding of a compact, connected 2-complex into a compact, connected, orientable 3-manifold. We are interested to know, to which extent K² determines (up to homeomorphism) its regular neighborhood N(f(K²)) ⊆ M³. We exhibit a list of four obstructions to uniqueness, and prove that in the absence of these, the regular neighborhoods are uniquely determined: Let f,K²,M³ be as above and assume M³ is prime and not a Poincaré-counterexample. If N(f(K²)) does not contain essential annuli and has connected boundary, then N is determined by K².

Keywords:

AMSC: 57M20, 57N10, 57M05, 20F05

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