Linking of letters and the lower central series of free groups

2020/06/01 by Jeff Monroe, Monroe, Jeff, Dev Sinha +1 · 1 citation
Mathematics · #20E05 #20F14 #55Q25 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.00989

openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop invariants of the lower central series of free groups through linking of letters, showing they span the rational linear dual of the lower central series subquotients. We build on an approach to Lie coalgebras through operads, setting the stage for generalization to the lower central series Lie algebra of any group. Our approach yields a new co-basis for free Lie algebras. We compare with the classical approach of Fox derivatives. v2: substantial refinement of exposition

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