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:
“And neigh like Boanerges—
Then—punctual as a Star
Stop—docile and omnipotent
At its own stable door—”
—Emily Dickinson (1830–1886)
“A poet is no rattlebrain, saying what comes uppermost, and, because he says every thing, saying, at last, something good; but a heart in unison with his time and country. There is nothing whimsical or fantastic in his production, but sweet and sad earnest, freighted with the weightiest convictions, and pointed with the most determined aim which any man or class knows of in his times.”
—Ralph Waldo Emerson (1803–1882)
“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)