• Corpus ID: 246035317

Classification of Consistent Systems of Handlebody Group Representations

  title={Classification of Consistent Systems of Handlebody Group Representations},
  author={Lukas Muller and Lukas Woike},
The classifying spaces of handlebody groups form a modular operad. Algebras over the handlebody operad yield systems of representations of handlebody groups that are compatible with gluing. We prove that algebras over the modular operad of handlebodies with values in an arbitrary symmetric monoidal bicategoryM (we introduce for these the name ansular functor) are equivalent to self-dual balanced braided algebras in M. After specialization to a linear framework, this proves that consistent… 


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