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:
“She saw
her five young children
writhe and die;
in that hour
she began to watch you,
she whose eyes are open forever.”
—Denise Levertov (b. 1923)
“What I would like to write is a book about nothing, a book without exterior attachments, which would be held together by the inner force of its style, as the earth without support is held in the air—a book that would have almost no subject or at least in which the subject would be almost invisible.”
—Gustave Flaubert (1821–1880)