Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

Euler characteristics for spaces of string links and the modular envelope of $\mathcal{L}_{\infty}$

Pages: 115 – 144

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a7


Paul Arnaud Songhafouo Tsopméné (Department of Mathematics and Statistics, University of Regina, Saskatchewan, Canada)

Victor Turchin (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)


We make calculations in graph homology which further understanding of the topology of spaces of string links, in particular, calculating the Euler characteristics of finite-dimensional summands in their homology and homotopy. In doing so, we also determine the supercharacter of the symmetric group action on the positive arity components of the modular envelope of $\mathcal{L}_{\infty} \textrm{.}$


string link, Euler characteristic, modular operad

2010 Mathematics Subject Classification

18D50, 57Q45

Supplemental Materials

Tables of Euler characteristics (pdf)

This work has been supported by Fonds de la Recherche Scientifique–FNRS (F.R.S.–FNRS), that the authors acknowledge. It has also been supported by the Kansas State University (KSU), where this paper was partially written during the stay of the first author, and which he thanks for hospitality. The second author is partially supported by the Simons Foundation “Collaboration grant for mathematicians,” award ID: 519474.

Received 8 September 2016

Received revised 10 November 2017

Published 16 May 2018