In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A^(2)_(3)-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which...In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A^(2)_(3)-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is homotopy equivalent to the homotopy fibre of the pinch map X∪CA→∑A.展开更多
Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well.We estimate the dimension of the stack M_(X)(nC,χ)of pure sheave...Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well.We estimate the dimension of the stack M_(X)(nC,χ)of pure sheaves supported at the non-reduced curve nC(n≥2)with C an integral curve on X.We prove that the Hilbert-Chow morphism h_(L,χ):M_(X)^(H)(L,χ)→|L|sending each semistable 1-dimensional sheaf to its support has all its fibers of the same dimension for X Fano or with the trivial canonical line bundle and|L|contains integral curves.展开更多
In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied.As an application,the structure of the homotopy set for self-maps of flag manifolds is determined.
An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We...An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We know that every sufficiently large 3-manifold can bc cut into some 3-cells along incompressible surfaces in a finite process. For a 3-manifold, it is interesting to know whether there exists an incompressible surface embedded in it and how the incompressible surface embeds.展开更多
In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of nume...In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of numerical Campedelli surfaces with fibrations of genus 2.展开更多
This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite cla...This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.展开更多
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly buil...On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.展开更多
The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained throu...The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained through studying the combinatorical properties of singular fibres. But with the rising of the genus of fibration, this method will not work now. In 1977, a more essential classification of singular fibres of genus two was given by Eiji Horikawa by using relative canonical maps. Prof. Xiao Gang has successfully improved the classification of Horikawa and effectively studied some algebra.ic surfaces by using his classification. We know that, ordinarily, through the classification of singular fibres, parameters of fibration can be obtained. Based on this, we study the properties of surfaces. But for some parameters, we can effectively describe them only by the study of combinatorical properties and topological展开更多
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) ...Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.展开更多
morphism. Harmonic morphisms may be characterized as harmonic mappings which are horizontally weakly conformal. In recent years a substantial progress has been made in the field of harmonic morphism, for example, refs...morphism. Harmonic morphisms may be characterized as harmonic mappings which are horizontally weakly conformal. In recent years a substantial progress has been made in the field of harmonic morphism, for example, refs. [ 3—7]. In ref. [4], Baird and Wood proved the following: (ⅰ) Any non-constant harmonic morphism from (S^3, g_(can)) to a Riemann展开更多
K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B ...K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B for a fixed map m: A→B. We have introduced a split fibration of categories L: H_b→H_B and proved L-|J, J-|L in [2]. This paper first extends P_B-|N_B to P_b_*-|N_Bb~# for any fixed map b:B→.Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H_b and H^b where H^b is the dual of H_b. One of our results is N_b-|P_b. This differs from P_B-|N_B.展开更多
K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split...K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split fibration of categories L: H_b → H_B and H_b possesses some construction as in H_B.展开更多
文摘目的探讨致纤维化细胞因子和炎症细胞因子在冻结肩发生中的可能作用。方法 2014年9月至2016年4月,20例冻结肩患者接受肩关节镜手术,其中原发性冻结肩10例(A组),继发性冻结肩10例(B组)。以同期接受肩关节镜手术的10例非冻结肩患者作为对照(C组)。q PCR检测肩关节滑膜组织中基质金属蛋白酶1(MMP1)、MMP3、肿瘤坏死因子-α(TNF-α)、白细胞介素-1(IL-1)、IL-6、IL-8、粒细胞巨噬细胞集落刺激因子(GM-CSF)和巨噬细胞集落刺激因子(M-CSF)m RNA表达水平。结果 A组和B组MMP1和MMP3 m RNA表达高于C组(P<0.05),TNF-α、IL-1、IL-6、IL-8、GM-CSF和M-CSF m RNA显著高于C组(P<0.001),A组和B组间各因子m RNA表达无显著性差异(P>0.05)。结论冻结肩的发生可能与患者关节滑膜组织中致纤维化细胞因子和炎症细胞因子的高表达有关。
基金supported by National Natural Science Foundation of China (Grant No. 11701430), supported by National Natural Science Foundation of China (Grant No. 11971461)。
文摘In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A^(2)_(3)-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is homotopy equivalent to the homotopy fibre of the pinch map X∪CA→∑A.
基金supported by National Natural Science Foundation of China(Grant Nos.21022107 and 11771229)。
文摘Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well.We estimate the dimension of the stack M_(X)(nC,χ)of pure sheaves supported at the non-reduced curve nC(n≥2)with C an integral curve on X.We prove that the Hilbert-Chow morphism h_(L,χ):M_(X)^(H)(L,χ)→|L|sending each semistable 1-dimensional sheaf to its support has all its fibers of the same dimension for X Fano or with the trivial canonical line bundle and|L|contains integral curves.
基金Supported by Chinese Post-Doctoral Scientific Foundation
文摘In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied.As an application,the structure of the homotopy set for self-maps of flag manifolds is determined.
文摘An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We know that every sufficiently large 3-manifold can bc cut into some 3-cells along incompressible surfaces in a finite process. For a 3-manifold, it is interesting to know whether there exists an incompressible surface embedded in it and how the incompressible surface embeds.
文摘In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of numerical Campedelli surfaces with fibrations of genus 2.
文摘This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10101004).
文摘On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
文摘The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained through studying the combinatorical properties of singular fibres. But with the rising of the genus of fibration, this method will not work now. In 1977, a more essential classification of singular fibres of genus two was given by Eiji Horikawa by using relative canonical maps. Prof. Xiao Gang has successfully improved the classification of Horikawa and effectively studied some algebra.ic surfaces by using his classification. We know that, ordinarily, through the classification of singular fibres, parameters of fibration can be obtained. Based on this, we study the properties of surfaces. But for some parameters, we can effectively describe them only by the study of combinatorical properties and topological
文摘Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.
文摘morphism. Harmonic morphisms may be characterized as harmonic mappings which are horizontally weakly conformal. In recent years a substantial progress has been made in the field of harmonic morphism, for example, refs. [ 3—7]. In ref. [4], Baird and Wood proved the following: (ⅰ) Any non-constant harmonic morphism from (S^3, g_(can)) to a Riemann
基金Supported by National Natural Science Foundation of China
文摘K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B for a fixed map m: A→B. We have introduced a split fibration of categories L: H_b→H_B and proved L-|J, J-|L in [2]. This paper first extends P_B-|N_B to P_b_*-|N_Bb~# for any fixed map b:B→.Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H_b and H^b where H^b is the dual of H_b. One of our results is N_b-|P_b. This differs from P_B-|N_B.
基金Supported by National Natural Science Foundation of Chinathe Doctoral Foundation of the National Educational Committee of China
文摘K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split fibration of categories L: H_b → H_B and H_b possesses some construction as in H_B.
