Related papers: On free global spectra

(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the passage from unstable to stable homotopy…

Using Cayley graphs and Clifford algebras, we are able to give, for every finitely generated groups, a uniform construction of spectral triples with a generically non-trivial phase for the Dirac operator. Unfortunatly $D_{+}$ is index $0$,…

Let G be a finite group. A collection P={H1, ..., Hr} of subgroups of G, where r > 1, is said a non-trivial partition of G if every non-identity element of G belongs to one and only one Hi, for some 1 <=i<=r. We call a group G that does not…

A non-isolated vertex $x\in V(G)$ is called $C_{3}$-free if $x$ belongs to no triangle of $G$. In \cite{BMW} Burger, Mynhardt and Weakley introduced the idea of universal fixers. Let $G=(V,E)$ be a graph with $n$ vertices and $G'$ a copy of…

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…

Let $G$ be the fundamental group of a graph of finitely generated virtually free groups with virtually cyclic edge groups. We shaw that $G$ is cohomologically good if $G$ is residually finite. If $G$ is LERF, we prove that G splits…

We introduce a notion of freeness for $RO$-graded equivariant generalized homology theories, considering spaces or spectra $E$ such that the $R$-homology of $E$ splits as a wedge of the $R$-homology of induced virtual representation…

Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely…

The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain $\Omega\subset\mathbb{R}^{3}$, given by \[ \left\{ \begin{array}{l} -\rm{div}(a\,\nabla u_{\omega}^{g})-\omega…

We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in…

The free automorphisms of a class of Reinhardt free spectrahedra are trivial.

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…

Let $G=*_\lambda G_\lambda$ be a free product of torsion-free groups, and let $g\in[G,G]$ be any element not conjugate into a $G_\lambda$. Then scl$_G(g)\ge1/2$. This generalizes, and gives a new proof of a theorem of Duncan-Howie.

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

We construct a new spectrum of units for a commutative symmetric ring spectrum that detects the difference between a periodic ring spectrum and its connective cover. It is augmented over the sphere spectrum. The homotopy cofiber of its…

We introduce generalizations of global equivariant spectra which encode globally equivariant cohomology theories equipped with additional transfers, such as the deflation maps present in equivariant topological $K$-theory. We call these…

A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point…

Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…

We approach a problem of realising algebraic objects in a certain universal equivariant stable homotopy theory; the global homotopy theory of Schwede. Specifically, for a global ring spectrum $R$, we consider which classes of ring…