Related papers: More noncommutative 4-spheres
A new diffeomorphism invariant of integral homology 3-spheres is defined using a non-abelian 'quaternionic' version of the Seiberg-Witten equations.
Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of…
We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of…
We present direct arguments for non-commutativity of spheres in the AdS/CFT correspondence. The discussion is based on results for the $S_N$ orbifold SCFT. Concentrating on three point correlations (at finite $N$) we exhibit a comparison…
We introduce a class of noncommutative spectra and give the sheaf structure on the class of noncommutative spectra.
A brief report on recent work on the sphere-packing problem.
Examples of nonformal simply connected symplectic manifolds are constructed.
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
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)
The real sphere $S^{N-1}_\mathbb R$ appears as increasing union, over $d\in\{1,...,N\}$, of its "polygonal" versions $S^{N-1,d-1}_\mathbb R=\{x\in S^{N-1}_\mathbb R|x_{i_0}... x_{i_d}=0,\forall i_0,...,i_d\ {\rm distinct}\}$. Motivated by…
Given n quaternions we investigate the extent of non-commutativity of their multiple products, commutators and exponential products.
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…
We present an infinite sequence of smooth embeddings of a connected sum of 6 projective planes in the 4-sphere, which are all ambient homeomorphic, but pairwise ambient non-diffeomorphic. The double covers of the 4-sphere ramified along…
We consider astrophysical objects such as main-sequence stars, white-dwarfs and neutron stars in a noncommutative context. Noncommutativity is implemented via a deformed dispersion relation $E^{2}=p^{2}c^{2}(1+\lambda E)^{2}+m^{2}c^{4}$…
The sphere $S^{N-1}_\mathbb R$ has a half-liberated analogue $S^{N-1}_{\mathbb R,*}$, and a free analogue $S^{N-1}_{\mathbb R,+}$. This is a presentation of the construction and main properties of these noncommutative spheres,…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.
This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.
In this contribution we discuss the Noncommutative Standard Model and the associated Standard Model-forbidden decays that can possibly serve as an experimental signature of space-time noncommutativity.
We show that there exist infinitely many pairwise non-isotopic splitting spheres for two unlinked, unknotted $S^2$'s in $S^4$. This answers a question posed by Hughes, Kim, and Miller.