Morita classes in the homology of automorphism groups of free groups

@inproceedings{Conant2004MoritaCI,
title={Morita classes in the homology of automorphism groups of free groups},
author={James Conant and Karen Vogtmann},
year={2004}
}

Using Kontsevich’s identification of the homology of the Lie algebra l∞ with the cohomology of Out(Fr), Morita defined a sequence of 4k–dimensional classes μk in the unstable rational homology of Out(F2k+2). He showed by a computer calculation that the first of these is non-trivial, so coincides with the unique non-trivial rational homology class for Out(F4). Using the “forested graph complex” introduced in [2], we reinterpret and generalize Morita’s cycles, obtaining an unstable cycle for… CONTINUE READING