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Philip Egger

Publications and source records attributed to Philip Egger.

3 recordsLinked to original sources
arXiv2019

A class of $2$-local finite spectra which admit a $v_2^1$-self-map

At the prime $2$, Behrens, Hill, Hopkins and Mahowald showed $M_2(1,4)$ admits $32$-periodic $v_2$-self-map and more recently authors joint with Mahowald showed $A_1$ also admits $32$-periodic $v_2$-self-map. This leads to the question, whether there exists a finite $2$-local complex with periodicity less than $32$. This paper will answer the question by producing a class of finite $2$-local spectra $\widetilde{\mathcal{Z}}$ all of which admit $1$-periodic $v_2$-self-map.

math.AT↗
arXiv2019

Towards the $K(2)$-local homotopy groups of $Z$

Recently we introduced a class $\widetilde{\mathcal{Z}}$ of $2$-local finite spectra and showed that all spectra $Z\in \widetilde{\mathcal{Z}}$ admit a $v_2$-self-map of periodicity $1$. The aim of this article is to compute the $K(2)$-local homotopy groups $π_*L_{K(2)}Z$ of all spectra $Z \in \widetilde{\mathcal{Z}}$ using a homotopy fixed point spectral sequence, and we give an almost complete computation. The incompleteness lies in the fact that we are unable to eliminate one family of $d_3$-differentials and a few potential hidden extensions, though we conjecture that all these differentials and hidden extensions are trivial.

math.AT↗