Hochschild-Pirashvili homology on suspensions and representations of Out(F_n)

2015/07/30 by Victor Turchin, Thomas Willwacher, Turchin, Victor +1 · 1 citation
Mathematics · #13D03 #19D55 #55N99 #Advanced Algebra and Geometry #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.1507.08483

openalex publication_date 2015/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Hochschild-Pirashvili homology on any suspension admits the so called Hodge splitting. For a map between suspensions f\colon ΣY→ ΣZ, the induced map in the Hochschild-Pirashvili homology preserves this splitting if f is a suspension. If f is not a suspension, we show that the splitting is preserved only as a filtration. As a special case, we obtain that the Hochschild-Pirashvili homology on wedges of circles produces new representations of Out(F_n) that do not factor in general through GL(n,Z). The obtained representations are naturally filtered in such a way that the action on the graded quotients does factor through GL(n,Z).

Citations

• Relative (non-)formality of the little cubes operads and the algebraic\n Cerf Lemma

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