Lusternik-Schnirelmann category of Spin{9}

dc.creatorIwase, Norio
dc.creatorKono, Akira
dc.date2005-07-23
dc.date.accessioned2026-07-07T05:21:58Z
dc.date.available2026-07-07T05:21:58Z
dc.descriptionLet G be a compact connected Lie group and p : E \to Σ^2V a principal G-bundle with a characteristic map α: A=ΣV \to G. By combining cone decomposition arguments in Iwase-Mimura-Nishimoto [3,5] with computations of higher Hopf invariants introduced in Iwase [8], we generalize the result in Iwase-Mimura [12]: Let {F_{i}|0 \leq i \leq m} be a cone-decomposition of G with a canonical structure map σ_{i} of cat(F_{i}) \leq i for i \leq m. We have cat(E) \leq \Max(m+n,m+2) for n \geq 1, if αis compressible into F_{n} \subseteq F_{m} \simeq G and H^{σ_n}_n(α) = 0, under a suitable compatibility condition. On the other hand, calculations of Hamanaka-Kono [3] and Ishitoya-Kono-Toda [5] on spinor groups yields a lower estimate for the L-S category of spinor groups by means of a new computable invariant Mwgt(-;{mathbb{F}_2}) which is stronger than wgt(-;{\mathbb{F}_2}) introduced in Rudyak [16] and Strom [18]. As a result, we obtain cat(Spin(9)) = Mwgt(Spin(9);\mathbb{F}_2) = 8 > 6 = wgt(Spin(9);\mathbb{F}_2).
dc.description12pages
dc.identifierhttps://arxiv.org/abs/math/0507491
dc.identifierhttp://arxiv.org/abs/math/0507491
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75884
dc.subjectAlgebraic Topology
dc.subject55M30; 55N20, 57T30
dc.titleLusternik-Schnirelmann category of Spin{9}
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