Related papers: Hodge-Riemann Relations for Polytopes: A Geometric…

We introduce the notion of H-equivariant Morita-Takeuchi theory for coalgebras with symmetries given by a Hopf algebra H. A cohomology theory is introduced which classifies the possible lifts of coactions on coalgebras to corresponding…

Recent work of Chen He has determined through GKM methods the Borel equivariant cohomology with rational coefficients of the isotropy action on a real Grassmannian and an real oriented Grassmannian through GKM methods. In this expository…

We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology…

We prove a version of the Hodge-Riemann bilinear relations for Schur polynomials of K\"ahler forms and for Schur polynomials of positive forms on a complex vector space.

The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.

If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism…

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…

For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this conjecture for hypertoric varieties, recovering the ring…

We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic relation associated to period integrals of a certain…

We introduce bounded cohomology for (pairs of) groupoids and develop homological algebra to deal with it. We generalise results of Ivanov, Frigerio and Pagliantini to this setting and show that (under topological conditions) the bounded…

The main result is that for a connected hyperbolic complete K\"ahler manifold with bounded geometry of order two and exactly one end, either the first compactly supported cohomology with values in the structure sheaf vanishes or the…

We compute the Borel equivariant cohomology ring of the left $K$-action on a homogeneous space $G/H$, where $G$ is a connected Lie group, $H$ and $K$ are closed, connected subgroups and $2$ and the torsion primes of the Lie groups are units…

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory.

This is a hands on introduction to McMullen's Polytope Algebra. More than interesting on its own, this algebra was McMullen's tool to give a combinatorial proof of the g-theorem.

Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory…

This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.

This paper explicitly describes Hodge structures of complete intersections of ample hypersurfaces in compact simplicial toric varieties.

Padberg introduced a geometric notion of ranks for (mixed) integer rational polyhedrons and conjectured that the geometric rank of the matching polytope is one. In this work, we prove that this conjecture is true.

The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well…