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N∞-operads
and associahedra
Scott Balchin, David Barnes and Constanze Roitzheim |
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Vol. 315 (2021), No. 2, 285–304
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DOI: 10.2140/pjm.2021.315.285
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Abstract |
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We provide a combinatorial approach to studying the collection of N∞-operads in G-equivariant homotopy theory for G a finite cyclic group of prime power order. In particular, we show that for G=Cpn the natural order on the collection of N∞-operads is in bijection with the poset structure of the (n+1)-associahedron. We further provide a lower bound for the number of possible N∞-operads for any finite cyclic group G. As such, we have reduced an intricate problem in equivariant homotopy theory to a manageable combinatorial problem. |
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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Authors |
| Scott Balchin | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| David Barnes | |
| Mathematical Sciences Research
Centre Queen’s University Belfast United Kingdom |
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| Constanze Roitzheim | |
| School of Mathematics, Statistics
and Actuarial Science University of Kent Canterbury United Kingdom |
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