A graduate textbook on stable homotopy theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press. Some corrections may be found here [July 2023].
These can be found on the arXiv.
Equivariant sheaves for profinite groups
D. Barnes and D. Sugrue.
Topology Appl., 319: Paper No. 108215, 37, 2022.
The equivalence between rational G-sheaves and rational G-Mackey functors for profinite G
D. Barnes and D. Sugrue.
Math. Proc. Cambridge Philos. Soc., 174(2):345–368, 2023.
S. Balchin, D. Barnes, and C. Roitzheim.
Pacific J. Math., 315(2):285–304, 2021.
An introduction to algebraic models for rational G-spectra
D. Barnes and M. Kędziorek.
In Equivariant topology and derived algebra, volume 474 of London Math. Soc.
Lecture Note Ser., pages 119–179. Cambridge Univ. Press, Cambridge, 2022.
D. Barnes, J. P. C. Greenlees, and Magdalena Kędziorek.
Math. Z., 297(3-4):1205–1235, 2021.
An algebraic model for rational toral G-spectra
D. Barnes, J. P. C. Greenlees, M. Kędziorek.
Algebr. Geom. Topol., 19(7):3541–3599, 2019.
An algebraic model for rational naïve-commutative G-equivariant ring spectra for finite G
D. Barnes, J. P. C. Greenlees and M. Kedziorek
Homology, Homotopy Appl., 21(1):73-93, 2019
Rational SO(2)-equivariant spectra
D. Barnes, J. P. C. Greenlees, M. Kedziorek, and B. Shipley
Algebr. Geom. Topol. , 17 (2017), no. 2, 983–1020
D. Barnes
J. Homotopy Relat. Struct. , 12 (2017), no. 4, 1009–1032
Rational O(2)-equivariant spectra
D. Barnes
Homology, Homotopy Appl., 19(1):225–252, 2017
A monoidal algebraic model for rational SO(2)-spectra
D. Barnes
Math. Proc. Cambridge Philos. Soc., 161(1):167–192, 2016
Comparing the orthogonal and homotopy functor calculi
D. Barnes and R. Eldred
J. Pure Appl. Algebra, 220(11):3650–3675, 2016
Capturing Goodwillie’s Derivative
D. Barnes and R. Eldred
J. Pure Appl. Algebra, 220(1):197–222, 2016
Stable left and right Bousfield localisations
D. Barnes and C. Roitzheim
Glasg. Math. J., 56(1):13-42, 2014
D. Barnes and C. Roitzheim
In An Alpine expedition through algebraic topology, volume 617 of Contemporary Mathematics, pages 13-30, 2014
Model Categories for Orthogonal Calculus
D. Barnes and P. Oman
Algebr. Geom. Topol., 13(2):959-999, 2013
Homological localisation of model categories
D. Barnes and C. Roitzheim
Applied Categorical Structures, pages 1-19, 2013
Monoidality of Franke's Exotic Model
D. Barnes and C. Roitzheim
Adv. Math., 228(6):3223-3248, 2011
Rational Z_p-Equivariant Spectra
D. Barnes
Algebr. Geom. Topol., 11(4):2107-2135, 2011
D. Barnes and C. Roitzheim
New York J. Math., 17:513-552, 2011
Classifying Rational G-Spectra for Finite G
D. Barnes
Homology, Homotopy Appl., 11(1):141-170, 2009
Splitting Monoidal Stable Model Categories
D. Barnes
J. Pure Appl. Algebra, 213(5):846-856, 2009