Related papers: A universal characterization of the Chern characte…
In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. We give a complete answer to this question in small dimensions, and also prove partial results without…
We study super parallel transport around super loops in a quotient stack, and show that this geometry constructs a global version of the equivariant Chern character.
Refinements of the transchromatic generalized character maps are constructed by taking into account the torus action on the inertia groupoid (also known as the Fix functor). The relationship between this construction and the geometry of…
The notion of a cyclic map g: A -> X is a natural generalization of a Gottlieb element in pi_n(X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which…
We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…
We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup. Such a classifying space gives us new counterexamples for the integral Hodge and Tate conjectures…
Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…
We study non-additive operations from algebraic Morava K-theories to oriented cohomology theories in algebraic geometry. For oriented cohomology theory $A$ that has a {$p^n$}-typical formal group law over a $\mathbb{Z}_{(p)}$-algebra we…
The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline…
In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete…
The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes…
A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected,…
We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{\`e}lic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic…
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. We are interested in giving a qualitative…
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…
The Chern number has been widely used to describe the topological properties of periodic structures in the momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
Notes for some talks given at the seminar on characteristic classes at NTNU in autumn 2006. In the paper a proof of the existence of a Chern-character from complex K-theory to any cohomology theory with values in graded Q-algebras is given.…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…