Christian Carrick

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20242026

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math.AT2026

The real Brown-Peterson homology of $I^c ◯^{I ¨} S^{I ¨ + 1}$

Christian Carrick, Bertrand Guillou, Sarah Petersen

We compute the $R O (C_{2})$ -graded real Brown--Peterson homology of the representation-loop space $I^c ◯^{I ¨} S^{I ¨ + 1}$ , where $I ¨ $ is the regular representation of the cyclic group of ord…

math.AT2025

Chromatic defect, Wood's theorem, and higher real $K$ -theories

Christian Carrick

Using Ravenel's Thom spectrum $X (n)$ , we introduce the concept of chromatic defect, which measures how far a spectrum is from being complex-orientable. We compute the chromatic def…

math.AT2025

Slice spectral sequences through synthetic spectra

Christian Carrick

We define a $t$ -structure on the category of filtered $G$ -spectra such that for a Borel $G$ -spectrum $X$ the slice filtration of $X$ is the connective cover of the homotopy fixed-p…

math.AT2024

On MU-homology of connective models of higher Real K-theories

Christian Carrick, Michael A. Hill

We use the slice filtration to study the $M U$ -homology of the fixed points of connective models of Lubin--Tate theory studied by Hill--Hopkins--Ravenel and Beaudry--Hill--Shi--Zeng…

The real Brown-Peterson homology of I^c◯I¨SI¨+1

Chromatic defect, Wood's theorem, and higher real K-theories

Slice spectral sequences through synthetic spectra

On MU-homology of connective models of higher Real K-theories

The real Brown-Peterson homology of $I^c ◯^{I ¨} S^{I ¨ + 1}$

Chromatic defect, Wood's theorem, and higher real $K$ -theories