Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Spanier–Whitehead duality in the $K(2)$-local category at $p=2$


Author: Irina Bobkova
Journal: Proc. Amer. Math. Soc. 148 (2020), 5421-5436
MSC (2010): Primary 55P25, 55P42, 55T25
DOI: https://doi.org/10.1090/proc/15078
Published electronically: September 4, 2020
MathSciNet review: 4163853
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The fixed point spectra of Morava $E$-theory $E_n$ under the action of finite subgroups of the Morava stabilizer group $\mathbb {G}_n$, and their $K(n)$-local Spanier–Whitehead duals can be used to approximate the $K(n)$-local sphere in certain cases. For any finite subgroup $F$ of $\mathbb {G}_2$ at $p=2$ we prove that the $K(2)$-local Spanier–Whitehead dual of the spectrum $E_2^{hF}$ is $\Sigma ^{44}E_2^{hF}$. These results are analogous to the known results at height 2 and $p=3$. The main computational tool we use is the topological duality resolution spectral sequence for the spectrum $E_2^{h\mathbb {S}_2^1}$ at $p=2$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55P25, 55P42, 55T25

Retrieve articles in all journals with MSC (2010): 55P25, 55P42, 55T25


Additional Information

Irina Bobkova
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
MR Author ID: 1124377
ORCID: 0000-0001-8775-2691
Email: ibobkova@math.tamu.edu

Received by editor(s): June 24, 2018
Received by editor(s) in revised form: December 24, 2018, July 2, 2019, and February 24, 2020
Published electronically: September 4, 2020
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No.  DMS-1440140, while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, CA, during the Spring 2019 semester, and Grant No. DMS-1638352 and DMS-2005627
Communicated by: Mark Behrens
Article copyright: © Copyright 2020 American Mathematical Society