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The 2-group of symmetries of a split chain complex

Author
Elgueta, J.
Type of activity
Report
Date
2010-12-15
Code
MAII-IR-10-00003
Repository
http://hdl.handle.net/2117/12410 Open in new window
Abstract
We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any {\it split} chain complex $A_{\bullet}$ in an arbitrary $\kb$-linear abelian category ($\kb$ any commutative ring with unit). In particular, it is shown that it is a {\it split} 2-group whose equivalence class depends only on the homology of $A_{\bullet}$, and that it is equivalent to the trivial 2-group when $A_\bullet$ is a split exact sequence. This provides a description of ...
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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