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:
“If it is to be done well, child-rearing requires, more than most activities of life, a good deal of decentering from one’s own needs and perspectives. Such decentering is relatively easy when a society is stable and when there is an extended, supportive structure that the parent can depend upon.”
—David Elkind (20th century)
“That’s how the Germans are.... The aristocrats at the top hard as glass, cold as ice, servants of the King, the working masses willing, pliable, sentimental, susceptible to brutality, the middle class educated and cowardly to the point of servility.”
—Alfred Döblin (1878–1957)
“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)