3-Manifolds with abelian embeddings in S4

Jonathan A. Hillman

Type: Article

Publication Date: 2019-12-13

Citations: 2

DOI: https://doi.org/10.1142/s0218216520500017

Abstract

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if $\pi_1(M)'$ is perfect, and that the embedding is then essentially unique.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Journal of Knot Theory and Its Ramifications - View

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Works Cited by This (20)

Action	Title	Year	Authors
+	Embedding Seifert Fibred 3-Manifolds and Sol<sup>3</sup> -Manifolds in 4-Space	1998	JS Crisp JA Hillman
+	Factorization of 3-manifolds	1962	D. B. A. Epstein
+	Embedding homology equivalent 3-manifolds in 4-space	1996	Jonathan A. Hillman
+	A vanishing theorem for Euler characteristics	1984	Shmuel Rosset
+ PDF Chat	Dehn’s lemma and handle decompositions of some 4-manifolds	1980	J Rubinstein
+	Trees of homotopy types of two-dimensional CW-complexes	1973	Micheal N. Dyer Allan J. Sieradski
+	A loop theorem for duality spaces and fibred ribbon knots	1983	Andrew Casson C. McA. Gordon
+ PDF Chat	Decomposition of $S^4$ As a Twisted Double of a Certain Manifold	1997	Yuichi Yamada
+	Four-manifolds, geometries and knots	2002	Jonathan A. Hillman
+	Poincare Complexes: I	1967	C. T. C. Wall