Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

$L$-homology on ball complexes and products

Pages: 11 – 40

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a2

Authors

Spiros Adams-Florou (Mathematics and Statistics, University of Glasgow, United Kingdom)

Tibor Macko (Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia)

Abstract

We construct homology theories with coefficients in $L$-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae which we hope will clarify products used in the theory of the total surgery obstruction.

Keywords

$L$-theory, surgery theory, ball complex

2010 Mathematics Subject Classification

57R65

Received 8 February 2017

Received revised 6 December 2017

Published 18 April 2018