Decompositions involving Anick's spaces

The fibre of the degree $3$ map, Anick spaces and the double suspension

Let $S^{2n+1}\{p\}$ denote the homotopy fibre of the degree $p$ self map of $S^{2n+1}$. For primes $p \ge 5$, work of Selick shows that $S^{2n+1}\{p\}$ admits a nontrivial loop space decomposition if and only if $n=1$ or $p$. Indecomposability in all but these dimensions was obtained by showing that a nontrivial decomposition of $ΩS^{2n+1}\{p\}$ implies the existence of a $p$-primary Kervaire invariant one element of order $p$ in $π_{2n(p-1)-2}^S$. We prove the converse of this last implication and observe that the homotopy decomposition problem for $ΩS^{2n+1}\{p\}$ is equivalent to the strong…

聚合同调积的安尼克猜想

Anick's conjecture for polyhedral products

本文通过研究聚合同调积的循环空间，验证了 Anick 对此类空间的猜想，并描述了其循环同调的加法结构。

Decompositions of suspensions of spaces involving polyhedral products

Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri, Bendersky, Cohen, and Gitler, and is a generalization of the retractile argument of James. The second decomposition is on the union of an arrangement of subspaces called diagonal subspaces, and generalizes the result of Labbasi.

Compactifications of Moduli Spaces and Cellular Decompositions

This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier work of Looijenga.