Related papers: The index of certain Stiefel manifolds

In this note, we compute the upper characteristic rank of the projective Stiefel manifolds over $\mathbb{R}, \mathbb{C}$ and $\mathbb{H}$ and the flip Stiefel manifolds. We also provide bounds for the $\mathrm{cup}$ lengths of these spaces.…

In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be…

A generalized Stiefel manifold is the manifold of orthonormal frames in a vector space with a non-degenerated bilinear or hermitian form. In this article, the Isometry group of the generalized Stiefel manifolds are computed at least up to…

We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe…

We consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We obtain a description of their tangent bundles, compute their mod p…

A well known quotient of the real Stiefel manifold is the projective Stiefel manifold. We introduce a new family of quotients of the real Stiefel manifold by cyclic group of order 2 whose action is induced by simultaneous pairwise flipping…

We give an index formula for the class of all *-maximally hypoelliptic differential operators on any closed manifold with vector bundle coefficients, generalising previous index formulas by Atiyah-Singer and van Erp. Using this formula, we…

We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…

We compute the degree of Stiefel manifolds, that is, the variety of orthonormal frames in a finite dimensional vector space. Our approach employs techniques from classical algebraic geometry, algebraic combinatorics, and classical invariant…

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…

Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion…

We obtain general formulae expressing Hirzebruch genera of a manifold with Z/p-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known…

In this paper, we compute the BP-cohomology of complex projective Stiefel manifolds. The method involves the homotopy fixed point spectral sequence, and works for complex oriented cohomology theories. We also use these calculations and…

This article describes a formula for second variation of generalized Einstein-Hilbert functional on Riemannian manifolds. This work extends the definition of stable Einstein manifolds, and we present some properties.

The flip Stiefel manifolds (FV_{m,2s}) are defined as the quotient of the real Stiefel manifolds (V_{m,2s}) induced by the simultaneous pairwise flipping of the co-ordinates by the cyclic group of order 2. We calculate the complex (K)-ring…

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local…

Let M be a foliated manifold and G a discrete group acting on M by diffeomorphisms mapping leaves to leaves. Then G naturally acts by automorphisms on the algebra of Heisenberg pseudodifferential operators on the foliation. Our main result…

In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of…

In this paper we study the $\Z/2$ action on real Grassmann manifolds $G_{n}(\R^{2n})$ and $\widetilde{G}_{n}(\R^{2n})$ given by taking (appropriately oriented) orthogonal complement. We completely evaluate the related $\Z/2$…