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:
“A horse, a buggy and several sets of harness, valued in all at about $250, were stolen last night from the stable of Howard Quinlan, near Kingsville. The county police are at work on the case, but so far no trace of either thieves or booty has been found.”
—H.L. (Henry Lewis)
“The prostitute is the scapegoat for everyone’s sins, and few people care whether she is justly treated or not. Good people have spent thousands of pounds in efforts to reform her, poets have written about her, essayists and orators have made her the subject of some of their most striking rhetoric; perhaps no class of people has been so much abused, and alternatively sentimentalized over as prostitutes have been but one thing they have never yet had, and that is simple legal justice.”
—Alison Neilans. “Justice for the Prostitute—Lady Astor’s Bill,” Equal Rights (September 19, 1925)
“No other group in America has so had their identity socialized out of existence as have black women.... When black people are talked about the focus tends to be on black men; and when women are talked about the focus tends to be on white women.”
—bell hooks (b. c. 1955)