On the Algebraic Foundations of Bounded Cohomology is popular PDF and ePub book, written by Theo Bühler in 2011, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, On the Algebraic Foundations of Bounded Cohomology can be Read Online from any device for your convenience.
On the Algebraic Foundations of Bounded Cohomology Book PDF Summary
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.
Detail Book of On the Algebraic Foundations of Bounded Cohomology PDF
- Author : Theo Bühler
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821853115
- Genre : Mathematics
- Total Page : 126 pages
- Language : English
- PDF File Size : 16,7 Mb
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