In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori. Open books have relevance to contact geometry, with a famous theorem of Emmanuel Giroux (given below) that shows that contact geometry can be studied from an entirely topological viewpoint.
Read more about Open Book Decomposition: Definition and Construction, Giroux Correspondence
Famous quotes containing the words open and/or book:
“Manuel showed her his open hand: “Look at this finger, how meager it seems, and this one even weaker, and this other one no stronger, and this one all by himself and on his own.”
Then he made a fist: “But now, is it strong enough, big enough, solid enough? It seems so doesn’t it?””
—Jacques Roumain (1907–1945)
“His eye had become minutely exact as to the book and its position. Then he resolved that he would not look at the book again, would not turn a glance on it unless it might be when he had made up his mind to reveal its contents.”
—Anthony Trollope (1815–1882)