### Genuine Equivariant Operads

- Series
- Geometry Topology Seminar
- Time
- Monday, October 22, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Luis Alexandre Pereira – Georgia Tech

A
fundamental result in equivariant homotopy theory due to Elmendorf
states that the homotopy theory of G-spaces, with w.e.s measured on all
ﬁxed points, is equivalent to the homotopy theory of G-coeﬃcient systems
in spaces, with w.e.s measured at each level
of the system. Furthermore, Elmendorf’s result is rather robust:
analogue results can be shown to hold for, among others, the categories
of (topological) categories and operads. However, it has been known for
some time that in the G-operad case such a result
does not capture the ”correct” notion of weak equivalence, a fact made
particularly clear in work of Blumberg and Hill discussing a whole
lattice of ”commutative operads with only some norms” that are not
distinguished at all by the notion of w.e. suggested
above. In this talk I will talk about part of a joint project which aims
at providing a more diagrammatic understanding of Blumberg and Hill’s
work using a notion of G-trees, which are a generalization of the trees
of Cisinski-Moerdijk-Weiss. More speciﬁcally,
I will describe a new algebraic structure, which we dub a ”genuine
equivariant operad”, which naturally arises from the study of G-trees
and which allows us to state the ”correct” analogue of Elmendorf’s
theorem for G-operads.