The authors prove that a 3-dimensional small cover M is a Haken manifold if and only if M is aspherical or equivalently the underlying simple polytope is a flag polytope.In addition,they find that M being Haken is als...The authors prove that a 3-dimensional small cover M is a Haken manifold if and only if M is aspherical or equivalently the underlying simple polytope is a flag polytope.In addition,they find that M being Haken is also equivalent to the existence of a Riemannian metric with non-positive sectional curvature on M.展开更多
Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn（λ） corresponding to the pair （Pn, λ） has a cell structure given by h. From this cell...Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn（λ） corresponding to the pair （Pn, λ） has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn（λ） with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ？n of this cellular chain complex and get that ？n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to （F, λF） is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ？k=0 or ±2 for 0 ≤ k 〈 n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn（λ）. Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion.展开更多
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
A small cover is a closed manifold M^n with a locally standard(Z_2)~n-action such that its orbit space is a simple convex polytope P^n. Let Δ~n denote an n-simplex and P(m) an m-gon. This paper gives formulas for cal...A small cover is a closed manifold M^n with a locally standard(Z_2)~n-action such that its orbit space is a simple convex polytope P^n. Let Δ~n denote an n-simplex and P(m) an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space Δ^(n_1)×Δ^(n_2)× P(m), where n_1 is odd.展开更多
The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura’s theorem on the const...The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura’s theorem on the construction of oriented 3-dimensional small covers and the L-Yu’s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.展开更多
In this paper, it is shown that for a 3-dimensional small cover M over a polytope P, there are only 2-torsions in H_1(M; Z). Moreover, the mod 2 Betti number growth of finite covers of M is studied.
In order to provide theoretical basis and data support for improving the production mode of covering,this study investigated the nighttime air temperature formed by multiple layers of films with tunnel sheds and small...In order to provide theoretical basis and data support for improving the production mode of covering,this study investigated the nighttime air temperature formed by multiple layers of films with tunnel sheds and small tunnel sheds as trial subjects.The experiment was carried out in four tunnel sheds with 0 or 2 small tunnel sheds covered by 0,1,2 and 3 layers of films,respectively in Jinan,Shandong Province in winter of 2018.The nighttime air temperatures of tunnel sheds and small tunnel sheds formed by 1,2,3 and 4 layers of plastic film were measured and analyzed to simulate the temperature environment of early-spring season.The results showed that there were little differences between the nighttime air temperatures inside the tunnel sheds which was installed 0-3-layer small tunnel sheds inside,and there were uncertainty in the values of the air temperatures inside and outside the tunnel sheds;and the nighttime temperature conditions were constantly improved with the number of plastic film layers increasing under the conditions of this study.The analysis indicated that the mechanism of raising the temperature surrounded by plastic film was not only due to its own thermal parameter (thermal conductivity).MATLAB fitting analysis results showed that the increment of nighttime temperature in multi-film coverings became smaller with the number of film layers increasing.In this study,the number of layers in multi-film covering should not exceed 5 layers.展开更多
基金supported by the National Natural Science Foundation of China(No.11871266)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The authors prove that a 3-dimensional small cover M is a Haken manifold if and only if M is aspherical or equivalently the underlying simple polytope is a flag polytope.In addition,they find that M being Haken is also equivalent to the existence of a Riemannian metric with non-positive sectional curvature on M.
基金Project supported by NSFC(Grant No.11401118)the program on the high level innovation team and outstanding scholars in universities of Guangxi province
文摘Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn（λ） corresponding to the pair （Pn, λ） has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn（λ） with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ？n of this cellular chain complex and get that ？n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to （F, λF） is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ？k=0 or ±2 for 0 ≤ k 〈 n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn（λ）. Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion.
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.
基金supported by the National Natural Science Foundation of China(No.11371118)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20121303110004)the Natural Science Foundation of Hebei Province(No.A2011205075)
文摘A small cover is a closed manifold M^n with a locally standard(Z_2)~n-action such that its orbit space is a simple convex polytope P^n. Let Δ~n denote an n-simplex and P(m) an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space Δ^(n_1)×Δ^(n_2)× P(m), where n_1 is odd.
基金Project supported by Fudan Universitythe Fujyukai Foundation and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2009-0063179)
文摘The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura’s theorem on the construction of oriented 3-dimensional small covers and the L-Yu’s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.
基金supported by the National Natural Science Foundation of China(Nos.11371094,11771088)
文摘In this paper, it is shown that for a 3-dimensional small cover M over a polytope P, there are only 2-torsions in H_1(M; Z). Moreover, the mod 2 Betti number growth of finite covers of M is studied.
基金Supported by the Department of Science and Technology,Government of India for their financial support of this work through the SERC Fast Track Scheme for Young Scientist(No.SR/FTP/MS-037/2011)
文摘在我们学习的这份报纸，一个薄垂直盘子的小摆动生产的表面波浪的产生的问题在深冰沉没了盖住的海洋。二个特别问题这里被认为 viz，波浪产生的问题由于一) 板和 b 滚动) 在一个固定垂直盘子前面的线来源的存在。全体的散发的波浪的振幅为两个问题，从板的距离被草地的合适的应用获得积分定理。这些然后为冰盖子参数的各种各样的值图形地被学习。
基金Supported by Weifang Comprehensive Experimental Station Project of National Watermelon and Melon Industrial Technology System(CARS-25)Agricultural Science and Technology Innovation Project of Shandong Academy of Agricultural Sciences(CXGC2018D05)
文摘In order to provide theoretical basis and data support for improving the production mode of covering,this study investigated the nighttime air temperature formed by multiple layers of films with tunnel sheds and small tunnel sheds as trial subjects.The experiment was carried out in four tunnel sheds with 0 or 2 small tunnel sheds covered by 0,1,2 and 3 layers of films,respectively in Jinan,Shandong Province in winter of 2018.The nighttime air temperatures of tunnel sheds and small tunnel sheds formed by 1,2,3 and 4 layers of plastic film were measured and analyzed to simulate the temperature environment of early-spring season.The results showed that there were little differences between the nighttime air temperatures inside the tunnel sheds which was installed 0-3-layer small tunnel sheds inside,and there were uncertainty in the values of the air temperatures inside and outside the tunnel sheds;and the nighttime temperature conditions were constantly improved with the number of plastic film layers increasing under the conditions of this study.The analysis indicated that the mechanism of raising the temperature surrounded by plastic film was not only due to its own thermal parameter (thermal conductivity).MATLAB fitting analysis results showed that the increment of nighttime temperature in multi-film coverings became smaller with the number of film layers increasing.In this study,the number of layers in multi-film covering should not exceed 5 layers.
