On a spectral sequence for the cohomology of infinite loop spaces by Haugseng, Rune Gjoringbo, Miller, Haynes R

“…We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield-Kan cosimplicial space giving the 2-nilpotent completion of a connective spectrum X. …”
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Computation of cohomology of Lie conformal and Poisson vertex algebras by Bakalov, Bojko, De Sole, Alberto, Kac, Victor G

“…Abstract We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. …”
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Quantum and Floer cohomology have the same ring structure by Piunikhin, Serguei

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Hochschild homology / cohomology of preprojective algebras of ADET quivers by Eu, Ching-Hwa

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The Novikov theory for symplectic cohomology and exact Lagrangian embeddings by Ritter, Alexander F. (Alexander Friedrich)

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Lie algebra cohomology and the representations of semisimple Lie groups by Vogan, David A., 1954-

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Cohomology and extensions of representations of groups with normal Engel subgroups by Kissin, Edward, Shulman, Victor

“…The paper studies the first cohomology group H1 (G, λ, U) under various spectral type conditions imposed on the restrictions of λ, U to N. …”
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Cohomology and torsion cycles over the maximal cyclotomic extension by Rössler, D, Szamuely, T

“…We show that this statement can be viewed as a particular case of a much more general one, namely that the absolute Galois group of K acts with finitely many fixed points on the étale cohomology with Q/Z-coefficients of a smooth proper K¯¯¯-variety defined over K. …”

Some new homology and cohomology theories of manifolds and orbifolds by Joyce, D

“…For each manifold or effective orbifold $Y$ and commutative ring $R$, we define a new homology theory $MH_*(Y;R)$, $M$-$homology$, and a new cohomology theory $MH^*(Y;R)$, $M$-$cohomology$. For $MH_*(Y;R)$ the chain complex $(MC_*(Y;R),\partial)$ is generated by quadruples $[V,n,s,t]$ satisfying relations, where $V$ is an oriented manifold with corners, $n\in\mathbb N$, and $s:V\to{\mathbb R}^n$, $t:V\to Y$ are smooth with $s$ proper near 0 in ${\mathbb R}^n$. …”

Kuranishi homology and Kuranishi cohomology: a User's Guide by Joyce, D

“…This gives major simplifications in Lagrangian Floer cohomology.…”

Deformations of Symplectic Cohomology and Exact Lagrangians in ALE Spaces by Ritter, A

Motivic action on coherent cohomology of Hilbert modular varieties by Horawa, A

“…We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. …”

Cohomology groups of deformations of line bundles on complex tori by Ben-Bassat, O, Solomon, N

“…The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. …”

Topological quantum field theory structure on symplectic cohomology by Ritter, A

Discrete Morse theory for computing cellular sheaf cohomology by Curry, J, Ghrist, R, Nanda, V

“…Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. …”

Cohomology of Fuchsian groups and non-Euclidean crystallographic groups by Hughes, S

“…For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology.…”

Cohomology pairings on singular quotients in geometric invariant theory by Jeffrey, L, Kiem, Y, Kirwan, F, Woolf, J

“…In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the same as stability (although we make some weaker assumptions on the action). …”

Formulae for line bundle cohomology on Calabi‐Yau threefolds by Constantin, A, Lukas, A

“…We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi‐Yau threefolds realised as complete intersections in products of projective spaces. …”

Index formulae for line bundle cohomology on complex surfaces by Brodie, CR, Constantin, A, Deen, R, Lukas, A

“…We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. …”

ELLIPTIC COHOMOLOGY [AFTER LANDWEBERSTONG, OCHANINE, WITTEN, AND OTHERS] by Segal, G