# introduction to spectral geometry

In the paper Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." In NIPS, vol. 14, pp. 585-591. 2001 The author uses methods from spectral geometry, specifically Laplace-Beltrami operator, after searching around about the topic of spectral geometry I found the lectures and books beyond my background. What are the background materials I need to study/read (Lecture notes-references-...) before reading a book or a lecture about spectral geometry?

• Looking at the paper, it is not clear to me how much spectral geometry you want to learn vs. just sticking to spectral graph theory. For spectral graph theory, check Fan Chung's book. For spectral geometry, I am not an expert, and it really depends what your background is. You might have to learn some basic differential geometry first, e.g. something like this text amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/…. – Sasho Nikolov Jul 16 '14 at 5:32
• Thanks a lot for your reply, concerning the amount I want to learn, I just wanted to gain enough intuition (geometric/algebraic) to justify the use of the operator. – Magellanea Jul 16 '14 at 11:29