Computational tools for twisted topological Hochschild homology of equivariant spectra

Katharine Adamyk; Teena Gerhardt; Kathryn Hess; Inbar Klang; Hana Jia Kong

doi:10.1016/j.topol.2022.108102

Computational tools for twisted topological Hochschild homology of equivariant spectra

Katharine Adamyk
, Teena Gerhardt
, Kathryn Hess
, Inbar Klang
, Hana Jia Kong

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which we apply to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum MUR. In particular, we construct an equivariant version of the Bökstedt spectral sequence, the formulation of which requires further development of the Hochschild homology of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson.

Original language	English
Article number	108102
Journal	Topology and its Applications
Volume	316
DOIs	https://doi.org/10.1016/j.topol.2022.108102
Publication status	Published - 1 Jul 2022
Externally published	Yes

Funding

This paper is one part of the authors' Women in Topology III project. A second part of that project appears in a separate article [1] . We are grateful to the organizers of the Women in Topology III workshop, as well as to the Hausdorff Research Institute for Mathematics, where much of this research was carried out. We are grateful to Mike Hill and Dylan Wilson for many enlightening discussions related to this work. We also thank Christy Hazel, Asaf Horev, Dan Isaksen, Clover May, and Foling Zou for helpful conversations. The authors also thank an anonymous referee for helpful comments and for catching an error in a previous draft. The second author was supported by NSF grant DMS-1810575 . The Women in Topology III workshop was supported by NSF grant DMS-1901795 , the AWM ADVANCE grant NSF HRD-1500481 , and Foundation Compositio Mathematica .

Funders	Funder number
AWM ADVANCE	HRD-1500481
Foundation Compositio Mathematica
National Science Foundation	DMS-1901795, DMS-1810575

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title = "Computational tools for twisted topological Hochschild homology of equivariant spectra",

abstract = "Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which we apply to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum MUR. In particular, we construct an equivariant version of the B{\"o}kstedt spectral sequence, the formulation of which requires further development of the Hochschild homology of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson.",

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AU - Adamyk, Katharine

AU - Gerhardt, Teena

AU - Hess, Kathryn

AU - Klang, Inbar

AU - Kong, Hana Jia

PY - 2022/7/1

Y1 - 2022/7/1

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AB - Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which we apply to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum MUR. In particular, we construct an equivariant version of the Bökstedt spectral sequence, the formulation of which requires further development of the Hochschild homology of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson.

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JO - Topology and its Applications

JF - Topology and its Applications

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ER -

Computational tools for twisted topological Hochschild homology of equivariant spectra

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