Illinois Journal of Mathematics

Homology lens spaces in topological 4-manifolds

Allan L. Edmonds

Full-text: Open access

Abstract

For a closed $4$-manifold $X^4$ and closed $3$-manifold $M^3$ we investigate the smallest integer $n$ (perhaps $n=\infty$) such that $M^3$ embeds in $\#_nX^4$, the connected sum of $n$ copies of $X^4$. It is proven that any lens space (or homology lens space) embeds topologically locally flatly in $\#_2({\mathbf C}P^2\#\ \overline {{\mathbf C}P}^2)$, in $\#_4 S^2\times S^2$ and in $\#_8 \mathbf{C}P^2$.

Article information

Source
Illinois J. Math., Volume 49, Number 3 (2005), 827-837.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138221

Digital Object Identifier
doi:10.1215/ijm/1258138221

Mathematical Reviews number (MathSciNet)
MR2210261

Zentralblatt MATH identifier
1086.57018

Subjects
Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]
Secondary: 57M35: Dehn's lemma, sphere theorem, loop theorem, asphericity 57N10: Topology of general 3-manifolds [See also 57Mxx]

Citation

Edmonds, Allan L. Homology lens spaces in topological 4-manifolds. Illinois J. Math. 49 (2005), no. 3, 827--837. doi:10.1215/ijm/1258138221. https://projecteuclid.org/euclid.ijm/1258138221


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