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:
“In verity ... we are the poor. This humanity we would claim for ourselves is the legacy, not only of the Enlightenment, but of the thousands and thousands of European peasants and poor townspeople who came here bringing their humanity and their sufferings with them. It is the absence of a stable upper class that is responsible for much of the vulgarity of the American scene. Should we blush before the visitor for this deficiency?”
—Mary McCarthy (1912–1989)
“Think of what our Nation stands for,
Books from Boots’ and country lanes,
Free speech, free passes, class distinction,
Democracy and proper drains.”
—Sir John Betjeman (1906–1984)
“It’s important to remember that feminism is no longer a group of organizations or leaders. It’s the expectations that parents have for their daughters, and their sons, too. It’s the way we talk about and treat one another. It’s who makes the money and who makes the compromises and who makes the dinner. It’s a state of mind. It’s the way we live now.”
—Anna Quindlen (20th century)