相关论文: Twisted Hochschild homology and MacLane homology

We prove vanishing results for unramified stable cohomology of finite groups of Lie type.

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

For a complete hyperbolic three manifold M, we consider the representations of its fundamental group obtained by composing a lift of the holonomy with complex finite dimensional representations of SL(2,C). We prove a vanishing result for…

In this paper we prove some vanishing theorems for the twisted Dolbeault cohomology of the complete flag varieties associated to a simple, simply connected algebraic group.

We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.

We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In…

We study the twisted Novikov homology of the complement of a complex hypersurface in general position at infinity. We give a self-contained topological proof of the vanishing (except possibly in the middle degree) of the twisted Novikov…

We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…

We calculate the Hochschild dimension of quantum hyperplanes using the twisted Hochschild homology.

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…

We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like the mean curvature and the length of the second fundamental form. Several homology vanishing results are given.…

We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Putman-Sam on the classical split groups. We state a…

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for…

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of all Podles quantum spheres relative to arbitary automorphisms. Our calculations are based on a free resolution due to Masuda, Nakagami…

We study the relation between the vanishing of Andr\'{e}-Quillen homology and complete intersection flat dimension and we extend some of the existing results in the literature.

Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology…

We investigate the structure of reduced triply graded link homology $\overline{\mathrm{HHH}}$ in the top/bottom three $T-$degrees for links arising as closures of positive/negative braids. Using a diagrammatic approach to the Hochschild…

Given a $k$--scheme $X$ that admits a tilting object $T$, we prove that the Hochschild (co-)homology of $X$ is isomorphic to that of $A= End_{X}(T)$. We treat more generally the relative case when $X$ is flat over an affine scheme $Y=\Spec…

Calm\`es and Fasel have shown that the twisted Witt groups of split flag varieties vanish in a large number of cases. For flag varieties over algebraically closed fields, we sharpen their result to an if-and-only-if statement. In…