Related papers: Principal fibrations over noncommutative spheres
The purpose of the paper is twofold: First, known results of the noncommutative spin geometry of the standard Podles sphere are extended by discussing Poincare duality and orientability. In the discussion of orientability, Hochschild…
We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which,…
We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes'…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with the examples of quantum weighted projective and lens spaces and…
We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to…
In this work we have shown precisely that the curvature of a 2-sphere introduces quantum features in the system through the introduction of the noncommutative (NC) parameter that appeared naturally via equations of motion. To obtain this…
We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature.…
Following the pattern of the Frobenius structure usually assigned to the 1-dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions. Starting from dimension $d=1$, all the spheres are commutative…
We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of the map from the ring of rational…
Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…
In this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle: the functions on the total space are deformed into a right module for the star…
We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…
New method (arXiv:2104.11930) is applied to construct cubic interactions of massless spin 4 and real scalar fields. In contrast with the case of massless spin 3 fields (arXiv:2208.05700, 2209.03678, 2210.02842) the procedure requires to use…
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(T_p M) for all p in M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we…
Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the…
We classify fibrations by integral plane projective rational quartic curves whose generic fibre is regular but admits a non-smooth point that is a canonical divisor. These fibrations can only exist in characteristic two. The geometric…
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
The sphere formula states that in an arbitrary finite abstract simplicial complex, the sum of the Euler characteristic of unit spheres centered at even-dimensional simplices is equal to the sum of the Euler characteristic of unit spheres…
An explicit construction of surfaces with flat normal bundle in the Euclidean space (unit hypersphere) in terms of solutions of certain linear system is proposed. In the case of 3-space our formulae can be viewed as the direct Lie sphere…