Abstract
Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology of \(\mathrm {coTHH}\) for coalgebras over the sphere spectrum. We construct a relative coBökstedt spectral sequence to study \(\mathrm {coTHH}\) of coalgebra spectra over any commutative ring spectrum R. Further, we use algebraic structures in this spectral sequence to complete some calculations of the homotopy groups of relative topological coHochschild homology.
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Notes
For instance, the coBökstedt spectral sequence converges when C is a suspension spectrum \(\Sigma _+^\infty X\) for simply connected X [3].
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Acknowledgements
These results are part of the author’s dissertation work, and as such the author would like to thank her advisor, Teena Gerhardt, for her help and guidance over the years. In addition, discussions with Maximilien Péroux and Özgür Bayındır about their work with coalgebras and conversations with Gabe Angelini-Knoll were particularly helpful.
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Communicated by Anna Marie Bohmann.
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Klanderman, S. Computations of relative topological coHochschild homology. J. Homotopy Relat. Struct. 17, 393–417 (2022). https://doi.org/10.1007/s40062-022-00312-z
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DOI: https://doi.org/10.1007/s40062-022-00312-z