相关论文: Pulling back the Gromoll-Meyer construction and mo…
We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…
We explicitly describe all SO(7)-invariant almost quaternion-Hermitian structures on the twistor space of the six sphere and determine the types of their intrinsic torsion.
The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to K\"ahler geometry by several authors. In this paper we replace the strong notions of totally geodesic…
We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge…
Extensions of the MSSM often predict the existence of new fermions and their scalar superpartners which are vectorlike with respect to the standard model gauge group but may be chiral under additional gauge factors. In this paper we explore…
We introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds $M^{2n}$, where $n=7$ or $8$, which are homeomorphic but not…
We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements,…
We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual finiteness, and -- for almost all primes $p$ -- $\mathbb{F}_p$-homology growth above the…
We study $SO(m)$ covariant Matrix realizations of $ \sum_{i=1}^{m} X_i^2 = 1 $ for even $m$ as candidate fuzzy odd spheres following hep-th/0101001. As for the fuzzy four sphere, these Matrix algebras contain more degrees of freedom than…
It is the aim of this paper to transfer to generalised geometry tools employed in the study of semi-Riemannian immersions, specializing at times to semi-Riemannian hypersurfaces. Given an exact Courant algebroid $E \to M$ and an immersion…
We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as $SO(5)$-equivariant projections of quantized coadjoint orbits of $SO(6)$. We show that they arise as solutions in…
The (4k+2)-dimensional Kervaire manifold is a closed, piecewise linear (PL) manifold with Kervaire invariant 1 and the same homology as the product of two (2k+1)-dimensional spheres. We show that a finite group of odd order acts freely on a…
We develop a geometric description of structured Gaussian beams, a form a structured light, by applying geometric quantisation and symplectic reduction to the 2D harmonic oscillator. Our results show that the geometric quantisation of the…
We present a construction of closed 7-manifolds of holonomy G_2, which generalises Kovalev's twisted connected sums by taking quotients of the pieces in the construction before gluing. This makes it possible to realise a wider range of…
We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampere (class 6-6), Goursat (class 6-7) and generic…
We provide the geometric construction of a series of generalized Schur algebras of any type via Borel-Moore homologies and equivariant K-groups of generalized Steinberg varieties. As applications, we obtain a Schur algebra analogue of the…
We classify the combinatorial types of Murai spheres in dimensions $1$ and $2$, thereby showing that the corresponding convex simple polytopes have Delzant realizations. Then we describe all chordal Murai spheres $\mathrm{Bier}_c(M)$ with…
The space of orientation-compatible almost complex structures on the six-dimensional sphere naturally contains a copy of seven-dimensional real projective space. We show that the inclusion induces an isomorphism on fundamental groups and…