Related papers: A comparison of spectral sequences computing unsta…

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…

We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group whose odd-primary v1-periodic homotopy groups remian to be computed. The main work is…

We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain…

Let p be an odd prime. Let G be a p-local finite group over the extraspecial p-group p_+^{1+2}. In this paper we study the cohomology and the stable splitting of their p-complete classifying space BG.

The quasi-normal mode (QNM) spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this…

In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is represented by $k_0h_{n} \in Ext_A^{3,p^nq+2pq+q}(\mathbb{Z}_p,\mathbb{Z}_p)$ in the Adams…

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable…

Let X be a finite, n-dimensional, r-connected CW complex. We prove the following theorem: If p \geq n/r is an odd prime, then the loop space homology Bockstein spectral sequence modulo p is a spectral sequence of universal enveloping…

Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.

The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain…

Fix a prime number p and a non-negative integer n. We prove that if a p-complete spectrum X satisfying a mild finiteness condition has the same mod p cohomology as BP<n> as a module over the Steenrod algebra, then X is weak homotopy…

We investigate implications of an old conjecture in unstable homotopy theory related to the Cohen-Moore-Neisendorfer theorem and a conjecture about the $\mathbf{E}_{2}$-topological Hochschild cohomology of certain Thom spectra (denoted $A$,…

We introduce the category Pstem[n] of n-stems, with a functor P[n] from spaces to Pstem[n]. This can be thought of as the n-th order homotopy groups of a space. We show how to associate to each simplicial n-stem Q an (n+1)-truncated…

We compute some R-motivic stable homotopy groups. For $s - w \leq 11$, we describe the motivic stable homotopy groups $\pi_{s,w}$ of a completion of the R-motivic sphere spectrum. We apply the $\rho$-Bockstein spectral sequence to obtain…

We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods…

In this paper we consider classifying spaces of a family of $p$-groups and we prove that mod $p$ cohomology enriched with Bockstein spectral sequences determines their homotopy type among $p$-completed CW-complexes. We end with some…

We show nilpotency and completeness results for the homotopy automorphisms of a marked n-stage for an unstable coalgebra. These objects figure in the moduli problem of unstable coalgebras. Our theorems extend classical work of Dror,…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

We investigate the homogeneity of topological subspaces of separable Hilbert space, akin to the spaces with all points rational or all points irrational, so-called Erd\H{o}s spaces. We provide a non-homogeneous example, that is based on one…

We compute the mod 2 homology of spin mapping class groups in the stable range. In earlier work we computed the stable mod p homology of the oriented mapping class group, and the methods and results here are very similar. The forgetful map…