Related papers: Some observations on the index of $C_p$-spaces

Let $p$ denote an odd prime. We show by example that the inequalities obtained in arXiv:1704.05827 for the behaviour of the cohomological index of a join of free $\Z/p$-actions are sharp. Namely, for all odd integers $k,l$ at least one of…

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a…

We construct a free $\mathbb{Z}_2$-manifold $X_n$ for a positive integer $n$ such that $w_1(X_n)^n \neq 0$, but there is no $\mathbb{Z}_2$-equivariant map from $S^2$ to $X_n$.

We study connected mod p finite A_p-spaces admitting AC_n-space structures with n<p for an odd prime p. Our result shows that if n is greator than (p-1)/2, then the mod p Steenrod algebra acts on the mod p cohomology of such a space in a…

For finite dimensional free $C_p$-spaces, the calculation of the Bredon cohomology ring as an algebra over the cohomology of $S^0$ is used to prove the non-existence of certain $C_p$-maps. These are related to Borsuk-Ulam type theorems, and…

We construct nontrivial examples of weak-$C_p$ ($1\leq p \leq \infty$) operator spaces with the local operator space structure very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are non-homogeneous Hilbertian operator spaces, and…

Let $G = \ZZ_p$, $p$ an odd prime, act freely on a finite-dimensional CW-complex $X$ with mod $p$ cohomology isomorphic to that of a lens space $L^{2m-1} (p;q_1,...,q_m)$. In this paper, we determine the mod $p$ cohomology ring of the orbit…

We provide counterexamples to P. Olver's freeness conjecture for $C^\infty$ actions. In fact, we show that a counterexample exists for any connected real Lie group with noncompact center, as well as for the additive group of the integers.

For each value of $p$ such that $0<p<1$, we give a specific example of two functions in the Hardy space $H^p$ and in the Bergman space $A^p$ that do not satisfy the triangle inequality. For Hardy spaces, this provides a much simpler proof…

We study abstract Ces\`aro spaces $CX$, which may be regarded as generalizations of Ces\`aro sequence spaces $ces_p$ and Ces\`aro function spaces $Ces_p(I)$ on $I = [0,1]$ or $I = [0,\infty)$, and also as the description of optimal domain…

By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quotients of a semisimple Lie group of dimension at most 10. In this paper we determine exactly which ones of these spaces actually admit such a…

We give a lower bound for the numerical index of the real space $L_p(\mu)$ showing, in particular, that it is non-zero for $p\neq 2$. In other words, it is shown that for every bounded linear operator $T$ on the real space $L_p(\mu)$, one…

Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We additionally provide a way to construct…

We compute the numerical index of the two-dimensional real $L_p$ space for $\frac65\leq p\leq \frac32$ and $3\leq p\leq 6$.

We determine a nice simple formula for the largest Euclidean space for which there is an orientable n-manifold with a nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove the analogue of the upper bound and…

We give examples of spaces which are good and bad at different primes in the sense of Bousfield and Kan in any arbitrary combination and investigate which impact the existence of a Sylow $p$-subgroup has on the homotopy type on the…

We study the index of nilpotency relative to certain Hecke operators in spaces of modular forms with integer weight and level $N$ with integer coefficients modulo primes $p$ for $(p, N) \in \{(3, 1), (5, 1), (7, 1), (3, 4)\}$. In these…

Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop…

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed…

On d\'emontre une conjecture due \`a N. Kuhn concernant la cohomologie singuli\`ere \`a coefficients mod p des espaces, comme module instable sur l'alg\`ebre de Steenrod. Notre d\'emonstration de ce r\'esultat, d\'ej\`a connu en…