In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifo...In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.展开更多
By means of the theory of Postnikov resolution, a sufficient condition for the existence of a kind of bundle maps is obtained. Some applications of the result are given. Particularly, it is proven that the deleted pro...By means of the theory of Postnikov resolution, a sufficient condition for the existence of a kind of bundle maps is obtained. Some applications of the result are given. Particularly, it is proven that the deleted products as well as configuration spaces of two simply connected manifolds with suitable dimension have the same homotopy type when the original manifolds are homotopically equivalent.展开更多
In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Gr...In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Grigor’yan,Yuri Muranov and Shing-Tung Yau.We show that the Mayer-Vietoris sequence theorem holds for Δ-twisted homology.Applying the Δ-twisted ideas to Cartesian products,we introduce the notion of Δ-twisted Cartesian product on simplicial sets,which generalizes the classical work of Barratt,Gugenheim and Moore on twisted Cartesian products of simplicial sets.Under certain hypothesis,we show that the coordinate projection of Δ-twisted Cartesian product admits a fibre bundle structure.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11371093,11431009 and 11661131004)supported by National Natural Science Foundation of China(Grant No.11028104)。
文摘In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.
文摘By means of the theory of Postnikov resolution, a sufficient condition for the existence of a kind of bundle maps is obtained. Some applications of the result are given. Particularly, it is proven that the deleted products as well as configuration spaces of two simply connected manifolds with suitable dimension have the same homotopy type when the original manifolds are homotopically equivalent.
基金Supported by NSFC(Grant No.11971144)High-level Scientific Research Foundation of Hebei Province+1 种基金the start-up research fund from BIMSAsupported by Postgraduate Innovation Funding Project of Hebei Province(Grant No.CXZZBS2022073)。
文摘In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Grigor’yan,Yuri Muranov and Shing-Tung Yau.We show that the Mayer-Vietoris sequence theorem holds for Δ-twisted homology.Applying the Δ-twisted ideas to Cartesian products,we introduce the notion of Δ-twisted Cartesian product on simplicial sets,which generalizes the classical work of Barratt,Gugenheim and Moore on twisted Cartesian products of simplicial sets.Under certain hypothesis,we show that the coordinate projection of Δ-twisted Cartesian product admits a fibre bundle structure.
