Is There a Term for a Manifold K(G,1)?

154 Views Asked by At

Is there a generally-accepted term (which has appeared "in print", in a peer-refereed, published paper) for a finitely-presented group G which has an aspherical, closed, connected, finite-dimensional manifold M for its K(G,1)?

1

There are 1 best solutions below

0
On BEST ANSWER

A quick google search gave "aspherical manifold groups" used in

Koji Fujiwara and Jason Fox Manning, "CAT(0) and CAT(−1) fillings of hyperbolic manifolds", J. Differential Geom. Volume 85, Number 2 (2010), 229-270.

However, this does not appear to be a common terminology. For instance, it is not used in the Manifold Atlas", http://www.map.mpim-bonn.mpg.de/Aspherical_manifolds, where such groups are consistently referred to as "the fundamental group of an aspherical closed manifold". Same in the survey

W. Lueck, "Aspherical manifolds", Bulletin of the AMS (2012) 1–17

Same in

Sylvain Cappell, Shmuel Weinberger and Min Yan, "Closed Aspherical Manifolds with Center" Journal of Topology 6 (2013) 1009–1018.

See also references I gave here in connection to the Wall Conjecture.

Thus, my suggestion is to stick with the more common terminology "the fundamental group of a closed aspherical manifold".