Department of Pure Mathematics

Department of Pure Maths
Mathematics Building, Block B
Xi'an Jiaotong-Liverpool University
111 Ren'ai Road Suzhou Dushu Lake Science and Education Innovation District , Suzhou Industrial Park
Suzhou,Jiangsu Province,P. R. China,215123

1. Critically paintable, choosable or colorable graphs

Author:Riasat, A;Schauz, U


Abstract:We extend results about critically k-colorable graphs to choosability and paintability (list colorability and on-line list colorability). Using a strong version of Brooks' Theorem, we generalize Gallai's Theorem about the structure of the low-degree subgraph of critically k-colorable graphs, and introduce a more adequate lowest-degree subgraph. We prove lower bounds for the edge density of critical graphs, and generalize Heawood's Map-Coloring Theorem about graphs on higher surfaces to paintability. We also show that on a fixed given surface, there are only finitely many critically k-paintable/k-choosable/k-colorable graphs, if k >= 6. In this situation, we can determine in polynomial time k-paintability, k-choosability and k-colorability, by giving a polynomial time coloring strategy for "Mrs. Correct". Our generalizations of k-choosability theorems also concern the treatment of non-constant list sizes (non-constant k). Finally, we use a Ramsey-type lemma to deduce all 2-paintable, 2-choosable, critically 3-paintable and critically 3-choosable graphs, with respect to vertex deletion and to edge deletion. (C) 2012 Elsevier B.V. All rights reserved.
2. Homogeneity-preserving property of harmonic sequences from surfaces into complex Grassmann manifolds

Author:Fei Jie;Zhang Wenjuan

Source:Frontiers of Mathematics in China,2017,Vol.12

Abstract:We prove that if phi is a homogeneous harmonic map from a Riemann surface M into a complex Grassmann manifold G(k,n), then the maps of the harmonic sequences generated by phi are all homogeneous.
3. Fundamental groups, homology equivalences and one-sided h-cobordisms

Author:Su Yang;Ye Shengkui

Source:Science China. Mathematics,2015,Vol.58

Abstract:We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes (manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
4. Low-dimensional representations of matrix groups and group actions on CAT(0) spaces and manifolds

Author:Ye, SK

Source:JOURNAL OF ALGEBRA,2014,Vol.409

Abstract:We study low-dimensional representations (rigidity problem) of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds. (C) 2014 Elsevier Inc. All rights reserved.
5. A Characterization of Homogeneous Holomorphic Two-Spheres in Qn

Author:Fei Jie;Wang Jun

Source:The Journal of Geometric Analysis,2019,Vol.31

Abstract:In this paper, we classify holomorphic curves in Qn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{doc...
6. Classification of polynomial mappings between commutative groups

Author:Schauz, U


Abstract:Some polynomials P with rational coefficients give rise to well defined maps between cyclic groups, Z(q) -> Z(r), x + qZ -> P(x) + rZ. More generally, there are polynomials in several variables with tuples of rational numbers as coefficients that induce maps between commutative groups. We characterize the polynomials with this property, and classify all maps between two given finite commutative groups that arise in this way. We also provide interpolation formulas and a Taylor-type theorem for the calculation of polynomials that describe given maps. (C) 2014 Elsevier Inc. All rights reserved.
7. Equivariant totally real 3-spheres in the complex projective space CPn

Author:Fei, J;Peng, CK;Xu, XW


Abstract:In this paper we study the equivariant totally real immersions from S-3 into CPn. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S-3/m(m+2)(3) into CPn, and characterize the minimal totally real isometric immersions from S-3/m(m+2)(3) into CPn by the standard example. We also give many minimal linearly full isometric immersions from S-1/5(3) into CP7. CP11 and CP15. As an application of our method, we classify equivariant Lagrangian S-3 in CP3 again. (C) 2012 Elsevier B.V. All rights reserved.
8. Classification of homogeneous minimal immersions from to

Author:Fei, J;He, L


Abstract:In this paper we determine all homogeneous minimal immersions of 2-spheres in quaternionic projective spaces .

Author:Zhang, WJ;Fei, J;Jiao, XX


Abstract:In this article, we determine all homogeneous two-spheres in the complex Grassmann manifold G(2, 5; C) by theory of unitary representations of the 3-dimensional special unitary group SU(2).
10. The action of matrix groups on aspherical manifolds

Author:Ye, SK


Abstract:Let SLn(Z) for n >= 3 be the special linear group and M-r be a closed aspherical manifold. It is proved that when r < n, a group action of SLn (Z) on M-r by homeomorphisms is trivial if and only if the induced group homomorphism SLn(Z) -> Out(pi(1)(M)) is trivial. For (almost) flat manifolds, we prove a similar result in terms of holonomy groups. In particular, when pi(1)(M) is nilpotent, the group SLn(Z) cannot act nontrivially on M when r < n. This confirms a conjecture related to Zimmer's program for these manifolds.
11. Trivial unit conjecture and homotopy theory

Author:Ye, SK

Source:JOURNAL OF ALGEBRA,2014,Vol.402

Abstract:A homotopy theoretic description is given for trivial unit conjecture in the group ring ZG. (C) 2013 Elsevier Inc. All rights reserved.
12. Vanishing of L-2-Betti numbers and failure of acylindrical hyperbolicity of matrix groups over rings

Author:Ji, F;Ye, SK


Abstract:Let R be an infinite commutative ring with identity and n >= 2 an integer. We prove that for each integer i = 0, 1, ... , n - 2, the L-2-Betti number b(i)((2)) (G) vanishes when G is the general linear group GL(n)(R), the special linear group SLn(R) or the group E-n(R) generated by elementary matrices. When R is an infinite principal ideal domain, similar results are obtained when G is the symplectic group Sp(2n)(R), the elementary symplectic group ESp(2n)(R), the split orthogonal group O(n, n)(R) or the elementary orthogonal group EO(n, n)(R ). Furthermore, we prove that G is not acylindrically hyperbolic if n >= 4. We also prove similar results for a class of noncommutative rings. The proofs are based on a notion of n-rigid rings.
13. Symmetries of flat manifolds, Jordan property and the general Zimmer program

Author:Ye, SK


Abstract:We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let G=En(R), EUn(R,?), SAut (Fn) or SOut (Fn). As applications, we prove that when n > 3 every group action of G on a closed flat manifold Mk (k
14. Rigidity of holomorphic curves in a hyperquadric Q(4)

Author:Fei, J;Wang, J


Abstract:In this paper, firstly, we obtain the Gauss equation and Codazzi equations of a holomorphic curve in a hyperquadric Q(n) and we also compute the Laplace of the square of the length of the second fundamental form. Secondly, we prove that any two linearly full holomorphic curves in Q(4) are congruent if their first and second fundamental forms are the same. Finally, we determine a one-parameter family of homogeneous holomorphic curves in Q(4) with constant curvature 2, but their second fundamental forms are different. (C) 2019 Elsevier B.V. All rights reserved.
15. Local rigidity of minimal surfaces in a hyperquadric Q(2)

Author:Fei, J;Wang, J


Abstract:In this paper, we study rigidity of a minimal immersion f from a surface M into a hyperquadric Q(2). It is proved that except a case that f is totally geodesic, totally real with Gauss curvature K = 0, then up to a rigidity, f is uniquely determined by the first fundamental form, the second fundamental form and Kahler angle. (C) 2018 Elsevier B.V. All rights reserved.
16. Homogeneous fibrations on log Calabi-Yau varieties

Author:Xu, JS


Abstract:We prove a structure theorem for the Albanese maps of varieties with Q-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.
17. Superminimal surfaces in hyperquadric Q_2

Author:Wang Jun;Fei Jie

Source:Frontiers of Mathematics in China,2020,Vol.15

Abstract:We study a superminimal surface M immersed into a hyperquadric Q_2 in several cases classified by two global defined functions tau_X and tau_Y, which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f: M Q_2. In case both tau_X and tau_Y are not identically zero, it is proved that f is superminimal if and only if f is totally real or io f: M CP~3 is also minimal, where i: Q_2 CP~3 is the standard inclusion map. In the rest case that tau_X = 0 or tau_Y = 0,the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q_2 are completely described.
18. Euler characteristics and actions of automorphism groups of free groups

Author:Ye, SK


Abstract:Let M-r be a connected orientable manifold with the Euler characteristic chi (M) not equivalent to 0 mod 6 . Denote by SAut(F-n) the unique subgroup of index two in the automorphism group of a free group. Then any group action of SAut(F-n) (and thus the special linear group SLn(Z)) with n >= r + 2 on M-r by homeomorphisms is trivial. This confirms a conjecture related to Zimmer's program for these manifolds.
19. Torus orbifolds with two fixed points


Source:Trends in Mathematics,2019,Vol.

Abstract:The main objects of this paper are torus orbifolds that have exactly two fixed points. We study the equivariant topological type of these orbifolds and consider when we can use the results of (Darby et al., Equivariant cohomology of torus orbifolds, arXiv:1809.03678 [8]) to compute its integral equivariant cohomology, in terms of generators and relations, coming from the corresponding orbifold torus graph.
20. On the growth rate of Rankin-Selberg series

Author:Su, F


Abstract:We define Rankin-Selberg series on general linear groups and study its growth rate by counting lattice points.
Total 41 results found
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