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:
“Man is not merely the sum of his masks. Behind the shifting face of personality is a hard nugget of self, a genetic gift.... The self is malleable but elastic, snapping back to its original shape like a rubber band. Mental illness is no myth, as some have claimed. It is a disturbance in our sense of possession of a stable inner self that survives its personae.”
—Camille Paglia (b. 1947)
“You see, after the war—and don’t forget it lasted a hundred years—thousands of us went from door to door, asking for honest work, and we were whipped for begging. The ruling class didn’t say, “Work or starve.” They said “Starve, for you shall not work.””
—Sonya Levien (1895–1960)
“No group and no government can properly prescribe precisely what should constitute the body of knowledge with which true education is concerned.”
—Franklin D. Roosevelt (1882–1945)