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:
“Speech and silence. We feel safer with a madman who talks than with one who cannot open his mouth.”
—E.M. Cioran (b. 1911)
“I don’t know but a book in a man’s brain is better off than a book bound in calf—at any rate it is safer from criticism. And taking a book off the brain, is akin to the ticklish & dangerous business of taking an old painting off a panel—you have to scrape off the whole brain in order to get at it with due safety—& even then, the painting may not be worth the trouble.”
—Herman Melville (1819–1891)