Computational tools for topological coHochschild homology

Anna Marie Bohmann; Teena Gerhardt; Amalie Høgenhaven; Brooke Shipley; Stephanie Ziegenhagen

doi:10.1016/j.topol.2017.12.008

Computational tools for topological coHochschild homology

Anna Marie Bohmann^*, Teena Gerhardt, Amalie Høgenhaven, Brooke Shipley, Stephanie Ziegenhagen

^*Corresponding author for this work

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

In recent work, Hess and Shipley [18] defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild–Kostant–Rosenberg type theorem in the cofree case for differential graded coalgebras. We also develop a coBökstedt spectral sequence to compute the homology of coTHH for coalgebra spectra. We use a coalgebra structure on this spectral sequence to produce several computations.

Original language	English
Journal	Topology and Its Applications
Volume	235
Pages (from-to)	185-213
Number of pages	29
ISSN	0166-8641
DOIs	https://doi.org/10.1016/j.topol.2017.12.008
Publication status	Published - 2018

Keywords

Coalgebra
Hochschild–Kostant–Rosenberg
Topological Hochschild homology

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10.1016/j.topol.2017.12.008

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title = "Computational tools for topological coHochschild homology",

abstract = "In recent work, Hess and Shipley [18] defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild–Kostant–Rosenberg type theorem in the cofree case for differential graded coalgebras. We also develop a coB{\"o}kstedt spectral sequence to compute the homology of coTHH for coalgebra spectra. We use a coalgebra structure on this spectral sequence to produce several computations.",

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author = "Bohmann, {Anna Marie} and Teena Gerhardt and Amalie H{\o}genhaven and Brooke Shipley and Stephanie Ziegenhagen",

year = "2018",

doi = "10.1016/j.topol.2017.12.008",

language = "English",

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journal = "Topology and its Applications",

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TY - JOUR

T1 - Computational tools for topological coHochschild homology

AU - Bohmann, Anna Marie

AU - Gerhardt, Teena

AU - Høgenhaven, Amalie

AU - Shipley, Brooke

AU - Ziegenhagen, Stephanie

PY - 2018

Y1 - 2018

N2 - In recent work, Hess and Shipley [18] defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild–Kostant–Rosenberg type theorem in the cofree case for differential graded coalgebras. We also develop a coBökstedt spectral sequence to compute the homology of coTHH for coalgebra spectra. We use a coalgebra structure on this spectral sequence to produce several computations.

AB - In recent work, Hess and Shipley [18] defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild–Kostant–Rosenberg type theorem in the cofree case for differential graded coalgebras. We also develop a coBökstedt spectral sequence to compute the homology of coTHH for coalgebra spectra. We use a coalgebra structure on this spectral sequence to produce several computations.

KW - Coalgebra

KW - Hochschild–Kostant–Rosenberg

KW - Topological Hochschild homology

UR - http://www.scopus.com/inward/record.url?scp=85037853717&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2017.12.008

DO - 10.1016/j.topol.2017.12.008

M3 - Journal article

AN - SCOPUS:85037853717

SN - 0166-8641

VL - 235

SP - 185

EP - 213

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Computational tools for topological coHochschild homology

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Keywords

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