Mod $p$ Decomposition of $H$-spaces of Low Rank

Yutaka Hemmi; Hirokazu Nishinobu

doi:10.4171/prims/178

JournalsprimsVol. 52, No. 2pp. 207–221

Mod $p$ Decomposition of $H$ -spaces of Low Rank

Yutaka Hemmi
Kochi University, Japan
Hirokazu Nishinobu
Kochi University, Japan

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Abstract

Let $X$ be a mod $p$ $H$ -space such that the mod $p$ cohomology is an exterior algebra generated by finitely many generators of degree $(2 n_{1} + 1, 2 n_{2} + 1, \dots, 2 n_{k} + 1)$ with $1 \leq n_{1} \leq n_{2} \leq \dots \leq n_{k}$ . It is known that if $n_{k} - n_{1} < p - 1$ then $X$ decomposes to a product of odd spheres, and if $n_{k} - n_{1} < 2 (p - 1)$ then $X$ decomposes to a product of odd spheres and $B_{n} (p)$ s. In the paper we consider the case of $n_{k} - n_{1} < 3 (p - 1)$ , and give a product decomposition of $X$ to irreducible factors.

Cite this article

Yutaka Hemmi, Hirokazu Nishinobu, Mod $p$ Decomposition of $H$ -spaces of Low Rank. Publ. Res. Inst. Math. Sci. 52 (2016), no. 2, pp. 207–221

DOI 10.4171/PRIMS/178