In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable re...In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.展开更多
In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.Lopez de Medrano concerned with the behavior of the moment-angle manifold under the surgery’cutting off a vertex...In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.Lopez de Medrano concerned with the behavior of the moment-angle manifold under the surgery’cutting off a vertex’on a simple polytope.Let P be a simple polytope of dimension n with m facets and Pv be a poly tope obtained from P by cutting off one vertex v.Let Z=Z(P)and Zv=Z(Pv)be the corresponding moment-angle manifolds.S.Gitler and S.Lopez de Medrano conjectured that:Zv is diffeomorphic to δ[(Z(-D^n+m)×D^2]##^m-n/j=1(m-n/j)(S^j+2×S^m+n-j-1),and they proved the conjecture in the case m<3 n.In this paper we prove the conjecture in the general case.展开更多
M?bius regular maps are surface embeddings of graphs with doubled edges such that(i)the automorphism group of the embedding acts regularly on flags and(ii) each doubled edge is a center of a M?bius band on the surface...M?bius regular maps are surface embeddings of graphs with doubled edges such that(i)the automorphism group of the embedding acts regularly on flags and(ii) each doubled edge is a center of a M?bius band on the surface. In this paper, we classify M?bius regular maps of order pq for any two primes p and q, where p≠q.展开更多
基金support of National Natural Science Foun- dation of China (Grant No. 10971144)Natural Science Foundation of Beijing (Grant No. 1092010)
文摘In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.
基金supported by National Natural Science Foundation of China(Grant Nos.11571186,11701411,11801580 and 11871284)。
文摘In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.Lopez de Medrano concerned with the behavior of the moment-angle manifold under the surgery’cutting off a vertex’on a simple polytope.Let P be a simple polytope of dimension n with m facets and Pv be a poly tope obtained from P by cutting off one vertex v.Let Z=Z(P)and Zv=Z(Pv)be the corresponding moment-angle manifolds.S.Gitler and S.Lopez de Medrano conjectured that:Zv is diffeomorphic to δ[(Z(-D^n+m)×D^2]##^m-n/j=1(m-n/j)(S^j+2×S^m+n-j-1),and they proved the conjecture in the case m<3 n.In this paper we prove the conjecture in the general case.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671276 and 11371259)
文摘M?bius regular maps are surface embeddings of graphs with doubled edges such that(i)the automorphism group of the embedding acts regularly on flags and(ii) each doubled edge is a center of a M?bius band on the surface. In this paper, we classify M?bius regular maps of order pq for any two primes p and q, where p≠q.
