ترغب بنشر مسار تعليمي؟ اضغط هنا

On the cohomology equivalences between bundle-type quasitoric manifolds over a cube

260   0   0.0 ( 0 )
 نشر من قبل Sho Hasui
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Sho Hasui




اسأل ChatGPT حول البحث

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) ($mathbb{C}P^2sharpmathbb{C}P^2$)-bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (2) quasitoric manifolds over $I^3$ are homeomorphic if their cohomology rings are isomorphic. In the latter case, there are only four quasitoric manifolds up to weakly equivariant homeomorphism which are not bundle-type.



قيم البحث

اقرأ أيضاً

401 - Sho Hasui 2013
A quasitoric manifold is a smooth manifold with a locally standard torus action for which the orbit space is identified with a simple polytope. For a class of topological spaces, the class is called strongly cohomologically rigid if any isomorphism o f cohomology rings can be realized as a homeomorphism. This paper shows the strong cohomological rigidity of the class of quasitoric manifolds over $I^3$.
243 - Sho Hasui 2013
For a simple $n$-polytope $P$, a quasitoric manifold over $P$ is a $2n$-dimensional smooth manifold with a locally standard action of the $n$-dimensional torus for which the orbit space is identified with $P$. This paper shows the topological classif ication of quasitoric manifolds over the dual cyclic polytope $C^n(m)^*$, when $n>3$ or $m-n=3$. Besides, we classify small covers, the real version of quasitoric manifolds, over all dual cyclic polytopes.
We show a homotopy decomposition of $p$-localized suspension $Sigma M_{(p)}$ of a quasitoric manifold $M$ by constructing power maps. As an application we investigate the $p$-localized suspension of the projection $pi$ from the moment-angle complex o nto $M$, from which we deduce its triviality for $p>dim M/2$. We also discuss non-triviality of $pi_{(p)}$ and $Sigma^inftypi$.
It is proved that if two quasitoric manifolds of dimension $le 2p^2-4$ for a prime $p$ have isomorphic cohomology rings, then they have the same $p$-local stable homotopy type.
We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds (or Bott towers) are toric manifolds over an $ n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $mathrm{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Odas $3$-fold, the simplest non-projective toric manifold, is over $mathrm{vc}(I^n)$. In this paper, we classify toric manifolds over $mathrm{vc}(I^n)$ $(nge 3)$ as varieties and also as smooth manifolds. As a consequence, it turns out that (1) there are many non-projective toric manifolds over $mathrm{vc}(I^n)$ but they are all diffeomorphic, and (2) toric manifolds over $mathrm{vc}(I^n)$ in some class are determined by their cohomology rings as varieties among toric manifolds.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا