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)
“The great disadvantage, and advantage, of the small urban bourgeois is his limited outlook. He sees the world as a middle- class world, and everything outside these limits is either laughable or slightly wicked.”
—George Orwell (1903–1950)
“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)