Contents Online
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
Authors
Abstract
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 $\mathcal{L}_{\infty} \textrm{.}$
Keywords
string link, Euler characteristic, modular operad
2010 Mathematics Subject Classification
18D50, 57Q45
Supplemental Materials
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