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:
“Revolutionary politics, revolutionary art, and oh, the revolutionary mind, is the dullest thing on earth. When we open a “revolutionary” review, or read a “revolutionary” speech, we yawn our heads off. It is true, there is nothing else. Everything is correctly, monotonously, dishearteningly “revolutionary.” What a stupid word! What a stale fuss!”
—Wyndham Lewis (1882–1957)
“Each had his past shut in him like the leaves of a book known to him by heart; and his friends could only read the title, James Spalding, or Charles Budgeon, and the passengers going the opposite way could read nothing at all—save “a man with a red moustache,” “a young man in grey smoking a pipe.””
—Virginia Woolf (1882–1941)