Morita classes in the homology of automorphism groups of free groups

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