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Abstract
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We provide a combinatorial approach to studying the collection of
-operads in
-equivariant
homotopy theory for
a finite cyclic group of prime power order. In particular, we show that for
the natural order on the
collection of
-operads
is in bijection with the poset structure of the
-associahedron.
We further provide a lower bound for the number of possible
-operads for any
finite cyclic group
.
As such, we have reduced an intricate problem in equivariant homotopy theory to a
manageable combinatorial problem.
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Keywords
operads, equivariant spectra, ring spectra, associahedra,
Catalan numbers
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Mathematical Subject Classification 2010
Primary: 18D50, 55P91
Secondary: 06A07, 52B20, 55N91
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Milestones
Received: 9 March 2020
Revised: 10 January 2021
Accepted: 8 July 2021
Published: 19 January 2022
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