On the Algebraic Foundation of Bounded Cohomology Paperback / softback
by Theo Buhler
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down.
The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category.
This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category.
The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures.
Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2011
- Category:
- ISBN:9780821853115
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2011
- Category:
- ISBN:9780821853115
