拟稳定正规可裂流形
Quasitoric stably normally split manifolds
摘要：
光滑稳定复流形称为完全切向/法向分裂流形（TTS/TNS-流形）。如果相应的复切向/法向量丛分别稳定同构于复线性丛的Whitney和，本文构造了流形$M$ s.t. $M$上的任何复向量丛稳定地等价于复线性丛的Whitney和。一个拟素流形也有这个性质当且仅当它是一个TNS-流形。通过$M$的上同调环中某些高次形式的非半定性，建立了一个新的准微分流形$M$的TNS-性质的判据.在拟流形族中，这推广了J. Lannes关于单连通稳定复TNS $4$ -流形的签名定理。我们应用我们的判据证明了复维数$3$的非奇异环面射影TNS-流形的矩多面体的旗性质。
英文摘要：
A smooth stably complex manifold is called a totally tangentially/normally split manifold (TTS/TNS-manifold, for short, resp.) if the respective complex tangential/normal vector bundle is stably isomorphic to a Whitney sum of complex linear bundles, resp. In this paper we construct manifolds $M$ s.t. any complex vector bundle over $M$ is stably equivalent to a Whitney sum of complex linear bundles. A quasitoric manifold shares this property iff it is a TNS-manifold. We establish a new criterion of the TNS-property for a quasitoric manifold $M$ via non-semidefiniteness of certain higher-degree forms in the respective cohomology ring of $M$. In the family of quasitoric manifolds, this generalises the theorem of J. Lannes about the signature of a simply connected stably complex TNS $4$-manifold. We apply our criterion to show the flag property of the moment polytope for a nonsingular toric projective TNS-manifold of complex dimension $3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
