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:
“Feminism, like Boston, is a state of mind. It is the state of mind of women who realize that their whole position in the social order is antiquated, as a woman cooking over an open fire with heavy iron pots would know that her entire housekeeping was out of date.”
—Rheta Childe Dorr (1866–1948)
“It is remarkable that, notwithstanding the universal favor with which the New Testament is outwardly received, and even the bigotry with which it is defended, there is no hospitality shown to, there is no appreciation of, the order of truth with which it deals. I know of no book that has so few readers. There is none so truly strange, and heretical, and unpopular. To Christians, no less than Greeks and Jews, it is foolishness and a stumbling-block.”
—Henry David Thoreau (1817–1862)