Related papers: Cone construction II
We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and…
We extend the computations in [AGM4] to find the mod 2 homology in degree 1 of a congruence subgroup Gamma of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is closely…
We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties. As a consequence, we obtain the vanishing…
The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. In terms of the representation…
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into…
We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures…
We construct a Kahler structure (which we call a generalised Kahler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those…
The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the…
We present the geometry lying behind counting twin prime polynomials in $\mathbb{F}_q[T]$ in general. We compute cohomology and explicitly count points by means of a twisted Lefschetz trace formula applied to these parametrizing varieties…
We revisit the nef curve cone theorem and use it to reprove the pseudo-effectivity of the second Chern classes for terminal weak Q-Fano varieties.
This is a revision of a paper first posted June 4, 2001. It will appear in the Journal of the AMS. In this paper we construct a small $E_\infty$ chain operad $\S$ which acts naturally on the normalized cochains $S^*X$ of a topological…
This is the first of two papers establishing structural properties of ${\cal R}_2$.
In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.
We determine the second homology group of the homological Goldman Lie algebra for an oriented surface.
Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic…
In this note, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result states that the holomorphic sections produced by the theorem are…
We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge-Riemann theorem for compact Kaehler manifolds.
This article is a continuation of "Quantum symmetry in multigraphs (part I)". In this article, we give an explicit construction of a non-Bichon type co-action on a multigraph that is, it preserves quantum symmetry of (V,E) in our sense but…
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.
As was shown by Harer the second homology of ${\mathbb M}_g$, the moduli space of compact Riemann surfaces of genus $g$, is of rank 1, provided $g \geq 3$. This means a nontrivial second de Rham cohomology class on ${\mathbb M}_g$ is unique…