Abstract
? | In 1987, Street showed how each simplex generated an $\omega$-category; that is,
a (possibly) infinite-dimensional category. This allowed a general definition of
the nerve of an $\omega$-category. The $\omega$-categories corresponding to
simplices were called {\em orientals}, and Street later developed the formalism
of {\em parity complex}, which abstracted the key features of these orientals,
and also included as examples the cubes and the globes (balls). Various other
researchers came up with alternative formalisms. All of them involve some sort
of combinatorial structure involving faces with a specified orientation, called
a parity.
The nestohedra are a family of polytopes which arose in work of de Concini and
Procesi. They include the simplices, the cubes, the associahedra (of Stasheff
and Tamari), and the permutohedra. I will consider these nestohedra as purely
combinatorial structures, and describe a general notion of parity for them.
This is joint work with Christopher Nguyen, which builds on material in his
thesis. |
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