Related papers: Vector Fields on certain quotients of complex Stie…
We study the Bott-Chern cohomology of complex orbifolds obtained as quotient of a compact complex manifold by a finite group of biholomorphisms.
We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we…
We describe the action of the different Frobenius morphisms on the cohomology ring of the moduli stack of algebraic vector bundles of fixed rank and determinant on an algebraic curve over a finite field in characteristic p and analyse…
We find an algorithm to compute the cohomology groups of spherical vector bundles on complex projective K3 surfaces, in terms of their Mukai vectors. In many good cases, we give significant simplifications of the algorithm. As an…
We compute the Stiefel-Whitney Classes for representations of dihedral groups $D_m$ in terms of character values of order two elements. We also provide criteria to identify representations V which lift to the double covers of the orthogonal…
In this work we extend some of the results of Ignat and Jerrard for Ginzburg-Landau vortices of tangent vector fields on two-dimensional Riemannian manifolds to the setting of complex hermitian line bundles. In particular, we elucidate the…
The purpose of this paper is two-fold: On the one side we would like to close a gap on the classification of vector bundles over $5$-manifolds. Therefore it will be necessary to study quaternionic line bundles over $5$-manifolds which are…
Let M be a paracompact smooth manifold, A a Weil algebra and M^A the associated Weil bundle. In this paper, we give another definition and characterization of vector field on M^A.
We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of…
We compute the mod-2 cohomology of the collection of all symmetric groups as a Hopf ring, where the second product is the transfer product of Strickland and Turner. We first give examples of related Hopf rings from invariant theory and…
We study a particular class of autonomous Differential-Algebraic Equations that are equivalent to Ordinary Differential Equations on manifolds. Under appropriate assumptions we determine an easy-to-use straightforward formula for the…
This paper computes the Fadell-Husseini index of Stiefel manifolds in the case where the group acts via permutations of the orthogonal vectors. The computations are carried out in the case of elementary Abelian $p$-groups. The results are…
In this article we develop the cotangent complex and (co)homology theories for spectral categories. Along the way, we reproduce standard model structures on spectral categories. As applications, we show that the invariants to descend to…
Hyperkahler quotients by non-free actions are typically highly singular, but are remarkably still partitioned into smooth hyperkahler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow…
Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…
The purpose of this paper is to investigate applications the covariant derivatives of the covector fields and killing vector fields with respect to the synectic lift a in a the Riemannian manifold to its tangent bundle, where Cg-complete…
The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of…
We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces.…