Wednesday, January 31, 2018

Riemann-Roch Theorem Redux

Riemann-Roch theorem is a mathematical assertion. It occurs in different branches suited to the occasion. Originally it is in complex analysis. There is a version for the surfaces. The version for algebraic varieties was given by Hirzebruch. The algebraic geometry version was given by Grothendiek. The version for higher genus is by Faltings. The investigations in Algebraic topology are associated with the names of Atiyah, Singer and Patodi. In Physics investigations by Edward Witten have very fundamental implications.

In this note we would like to demystify some of the aura associated with this fundamental and deep result in a plain language to the extent possible with our capabilities. We shall take up the topic from the point of view of the above mentioned different contexts and go through them.

(Developing article)