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

Mod pp Decomposition of HH-spaces of Low Rank

  • Yutaka Hemmi

    Kochi University, Japan
  • Hirokazu Nishinobu

    Kochi University, Japan
Mod $p$ Decomposition of $H$-spaces of Low Rank cover
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Abstract

Let XX be a mod pp HH-space such that the mod pp cohomology is an exterior algebra generated by finitely many generators of degree (2n1+1,2n2+1,,2nk+1)(2n_1+1, 2n_2+1, \dots, 2n_k+1) with 1n1n2nk1 \le n_1 \le n_2 \le \cdots \le n_k. It is known that if nkn1<p1n_k-n_1 < p-1 then XX decomposes to a product of odd spheres, and if nkn1<2(p1)n_k-n_1 < 2 (p-1) then XX decomposes to a product of odd spheres and Bn(p)B_n(p)s. In the paper we consider the case of nkn1<3(p1)n_k-n_1 < 3 (p-1), and give a product decomposition of XX to irreducible factors.

Cite this article

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

DOI 10.4171/PRIMS/178