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:
“Why the jailer does not leave open his prison doors,—why the judge does not dismiss his case,—why the preacher does not dismiss his congregation! It is because they do not obey the hint God gives them, nor accept the pardon which he freely offers to all.”
—Henry David Thoreau (1817–1862)
“If the book is good, is about something that you know, and is truly written, and reading it over you see that this is so, you can let the boys yip and the noise will have that pleasant sound coyotes make on a very cold night when they are out in the snow and you are in your own cabin that you have built or paid for with your work.”
—Ernest Hemingway (1899–1961)