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Aug 17, 2017 at 15:39 history bumped CommunityBot This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
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Feb 18, 2017 at 21:20 comment added Ryan Budney Your question seems a little vague. Yes, certainly there are other assumptions that would get you to your conclusion. . . but that isn't very specific. Could you focus your question a little bit?
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Dec 20, 2016 at 15:28 comment added Danny Ruberman Perhaps you could provide some context for the question; does it come from some particular circumstance? There is a 3-manifold that is a connected sum as described. Do you know something else? Are you given some information about a 4-manifold that it bounds?
Dec 20, 2016 at 10:44 history edited Topology Student CC BY-SA 3.0
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Dec 20, 2016 at 5:22 answer added David Snyder timeline score: 1
Dec 19, 2016 at 23:07 comment added Topology Student I am interested in keeping the $M$ has $\pi_1(M) < \infty$ and $\partial M$ is a connected sum of elliptic manifolds and $S^2 \times S^1$'s conditions. I would like to know what some sufficient conditions for $\partial M$ to be an elliptic manifold are. The assumption that $\partial M$ is incompressible, which with $\pi_1(M) < \infty$ implies $\pi_1(\partial M) < \infty$, seems too strong as it supersedes the other condition on $\partial M$.
Dec 18, 2016 at 21:11 comment added Danny Ruberman I'm not sure I understand the question; which hypotheses do you want to delete and which do you want to retain. Also, why does $\partial M$ being incompressible and also a sum of spherical manifolds imply that there's only one summand?
Dec 18, 2016 at 14:28 comment added Topology Student By incompressible I meant that the homomorphism between fundamental groups induced by the inclusion map $i:\partial M \rightarrow M$ is injective.
Dec 18, 2016 at 7:54 comment added Ryan Budney What convention are you using for a 4-manifold having an incompressible boundary?
Dec 18, 2016 at 1:57 history edited Topology Student CC BY-SA 3.0
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Dec 18, 2016 at 1:50 history asked Topology Student CC BY-SA 3.0