Cohomology of symmetric space

Abstract

In this thesis, we compute the De Rham cohomology of symmetric space with cohomology coefficients in C. The method we use is related to representation theory and combinatorics. For the classical cases, all cases are presented with a way to determine their cohomology. For exceptional cases except for type e₇ and e₈, the problem is partially by computer program. It is possible since in these finite cases, the dimensions are small. Although there are also only finitely many cases in type e₇ and e₈, their cohomology is not presented here since the dimensions of such spaces are too large for direct computation.

Date of Award	2016
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology