Operad groups and their finiteness properties

2014/09/03 by Thumann, Werner · 2 citations
#18D50 #20F05 #20F65 #57M07 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1409.1085

Abstract

We propose a new unifying framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application, we proof a theorem which implies that planar or symmetric or braided operads with transformations satisfying some finiteness conditions yield operad groups of type F_∞. This unifies and extends existing proofs that certain Thompson-like groups are of type F_∞.

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