Stable Mapping Class Group
One can embed the surface of genus g and 1 boundary component into by attaching an additional hole on the end (i.e., gluing together and ), and thus automorphisms of the small surface fixing the boundary extend to the larger surface. Taking the direct limit of these groups and inclusions yields the stable mapping class group, whose rational cohomology ring was conjectured by David Mumford (one of conjectures called the Mumford conjectures). The integral (not just rational) cohomology ring was computed in 2002 by Madsen and Weiss, proving Mumford's conjecture.
Read more about this topic: Mapping Class Group
Famous quotes containing the words stable, class and/or group:
“This stable is a Prince’s court.
This crib His chair of state;
The beasts are parcel of His pomp,
The wooden dish His plate.”
—Robert Southwell (1561?–1595)
“Money couldn’t buy friends, but you got a better class of enemy.”
—Spike Milligan (b. 1918)
“Unless a group of workers know their work is under surveillance, that they are being rated as fairly as human beings, with the fallibility that goes with human judgment, can rate them, and that at least an attempt is made to measure their worth to an organization in relative terms, they are likely to sink back on length of service as the sole reason for retention and promotion.”
—Mary Barnett Gilson (1877–?)