## A Higman embedding preserving asphericity

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- by Mark Sapir PDF
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## Abstract:

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical manifold $M$ such that the fundamental group $\pi _1(M)$ coarsely contains an expander. Thus it has infinite asymptotic dimension, is not coarsely embeddable into a Hilbert space, does not satisfy G. Yuâ€™s property A, and does not satisfy the Baum-Connes conjecture with coefficients. Closed aspherical manifolds with any of these properties were previously unknown.## References

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## Additional Information

**Mark Sapir**- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- MR Author ID: 189574
- Email: m.sapir@vanderbilt.edu
- Received by editor(s): April 26, 2011
- Received by editor(s) in revised form: September 22, 2011, November 29, 2011, and April 29, 2013
- Published electronically: July 9, 2013
- Additional Notes: This research was supported in part by NSF grant DMS-0700811.
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**27**(2014), 1-42 - MSC (2010): Primary 20F65; Secondary 20F69, 20F38, 22F50
- DOI: https://doi.org/10.1090/S0894-0347-2013-00776-6
- MathSciNet review: 3110794