Contents
Front Cover (OFC, IFC) and matter
COM volume 156 Issue 1 Cover and Front matter
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- 06 December 2019, pp. f1-f3
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Research Article
Loose Engel structures
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- 06 January 2020, pp. 412-434
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This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete
$h$-principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data.
Stability in the high-dimensional cohomology of congruence subgroups
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- 24 March 2020, pp. 822-861
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We prove a representation stability result for the codimension-one cohomology of the level-three congruence subgroup of
$\mathbf{SL}_{n}(\mathbb{Z})$. This is a special case of a question of Church, Farb, and Putman which we make more precise. Our methods involve proving finiteness properties of the Steinberg module for the group 
$\mathbf{SL}_{n}(K)$ for 
$K$ a field. This also lets us give a new proof of Ash, Putman, and Sam’s homological vanishing theorem for the Steinberg module. We also prove an integral refinement of Church and Putman’s homological vanishing theorem for the Steinberg module for the group 
$\mathbf{SL}_{n}(\mathbb{Z})$.
Relative cubulations and groups with a 2-sphere boundary
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- 24 March 2020, pp. 862-867
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We introduce a new kind of action of a relatively hyperbolic group on a
$\text{CAT}(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.
Front Cover (OFC, IFC) and matter
COM volume 156 issue 12 Cover and Front matter
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- Published online by Cambridge University Press:
- 23 February 2021, pp. f1-f4
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COM volume 156 Issue 8 Cover and Front matter
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- Published online by Cambridge University Press:
- 23 October 2020, pp. f1-f4
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Back Cover (IBC, OBC) and matter
COM volume 156 issue 11 Cover and Back matter
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- Published online by Cambridge University Press:
- 29 December 2020, pp. b1-b2
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Back Cover (OBC, IBC) and matter
COM volume 156 Issue 3 Cover and Back matter
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- 18 February 2020, pp. b1-b2
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Front Cover (OFC, IFC) and matter
COM volume 156 Issue 2 Cover and Front matter
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- 23 January 2020, pp. f1-f3
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Corrigendum
Corrigendum: On the probabilities of local behaviors in abelian field extensions
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- 15 May 2020, p. 1078
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Back Cover (OBC, IBC) and matter
COM volume 156 Issue 1 Cover and Back matter
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- Published online by Cambridge University Press:
- 06 December 2019, pp. b1-b2
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COM volume 156 Issue 7 Cover and Back matter
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- Published online by Cambridge University Press:
- 27 July 2020, pp. b1-b2
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COM volume 156 Issue 2 Cover and Back matter
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- Published online by Cambridge University Press:
- 23 January 2020, pp. b1-b2
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Back Cover (IBC, OBC) and matter
COM volume 156 issue 12 Cover and Back matter
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- Published online by Cambridge University Press:
- 23 February 2021, pp. b1-b2
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Front Cover (OFC, IFC) and matter
COM volume 156 Issue 5 Cover and Front matter
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- Published online by Cambridge University Press:
- 15 May 2020, pp. f1-f3
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COM volume 156 Issue 4 Cover and Front matter
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- Published online by Cambridge University Press:
- 14 April 2020, pp. f1-f3
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Back Cover (OBC, IBC) and matter
COM volume 156 Issue 8 Cover and Back matter
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- Published online by Cambridge University Press:
- 23 October 2020, pp. b1-b2
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COM volume 156 Issue 5 Cover and Back matter
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- Published online by Cambridge University Press:
- 15 May 2020, pp. b1-b2
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COM volume 156 Issue 4 Cover and Back matter
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- Published online by Cambridge University Press:
- 14 April 2020, pp. b1-b2
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