Related papers: The characteristic classes and Weyl invariants of …
The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of…
Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…
We compute all the spin fake degrees for the exceptional Weyl groups, which are by definition the graded multiplicities of the simple modules of a spin Weyl group in its spin coinvariant algebra. The spin fake degrees are all shown to be…
We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8…
We derive the Weierstrass (or spinor) representation for surfaces in three-dimensional Lie groups Nil, \tilde{SL}_2, and Sol with Thurston's geometries and establish the generating equations for minimal surfaces in these groups. By using…
After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first…
A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic group defined over a perfect field was given in \cite{Helm2000} using $3$ invariants. In \cite{HWD04,Helm-Wu2002} a full classification of…
We consider tilings of the plane with 12-fold symmetry obtained by the cut and projection method. We compute their cohomology groups using the techniques introduced by the second author, Hunton and Kellendonk. To do this we completely…
We define the tautological ring as the subring of the Chow ring of a Shimura variety generated by all Chern classes of all automorphic bundles. We explain its structure for the special fiber of a good reduction of a Shimura variety of Hodge…
Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin$^c$, spin$^{w_2}$ and orientable 12-manifolds respectively. We relate them to $\eta$-invariants when the…
We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{\xi_1,...,\xi_s\}$. We use this sequence to…
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…
We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples. The first class of examples consists of noncommutative manifolds associated with the so called $\theta$-deformations…
For a proper smooth variety of even dimension over a field of characteristic different from 2 or l, the second Stiefel-Whitney class of the l-adic cohomology and the second Hasse-Witt class of the de Rham cohomology are both defined in the…
We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit…
The groups of differential characters of Cheeger and Simons admit a natural multiplicative structure. The map given by the squares of degree 2k differential characters reduces to a homomorphism of ordinary cohomology groups. We prove that…
We explain how to exploit Rost's theory of Chow groups with coefficients to carry some computations of cohomological invariants (i.e. characteristic classes for G-torsors in Galois cohomology, for an algebraic group G). In particular, we…
A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…
A representation of general translation-invariant star products in the algebra of M(C) = lim_N\to \infty M_N (C) is introduced which results in the Moyal-Weyl-Wigner quantization. It provides a matrix model for general translation-invariant…
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…