Associahedra, Cyclohedra and a Topological solution to the A {infty}-Deligne conjecture - Mathematics > Algebraic TopologyReport as inadecuate




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Abstract: We give a topological solution to the $\Ainf$ Deligne conjecture usingassociahedra and cyclohedra. For this we construct three CW complexes whosecells are indexed by products of polytopes. Giving new explicit realizations ofthe polytopes in terms of different types of trees, we are able to show thatthe CW complexes are cell models for the little discs. The cellular chains ofone complex in particular, which is built out of associahedra and cyclohedra,naturally acts on the Hochschild cochains of an $\Ainf$ algebra yielding anexplicit, topological and minimal solution to the $\Ainf$ Deligne conjecture.Along the way we obtain new results about the cyclohedra, such as a newdecompositions into products of cubes and simplices, which can be used torealize them via a new iterated blow-up construction.



Author: Ralph M. Kaufmann, Rachel Schwell

Source: https://arxiv.org/







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