An interpretation of $E_n$-homology as functor homology

Birgit Richter (University of Hamburg)

Monday 25th January, 2010 16:00-17:00 Mathematics Building, room 204


I will (try to) motivate why the category of $n$-trees arises in the context of $E_n$-homology. Here, $E_n$ denotes the chain complex version of the operad of little $n$-cubes. The latter plays a crucial role in the study of $n$-fold loop spaces. Expressions in the $n$-fold bar construction of a commutative algebra directly relate to trees with $n$ layers. Using a suitable category of $n$-trees, Muriel Livernet and I could show that Benoit Fresse's notion of $E_n$-homology has a description in terms of functor homology.

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