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1.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):59-83
Let M n be a closed orientable manifold of dimension greater than three and G 1(M n ) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n ) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n ). 相似文献
2.
For a given manifold M we consider the non-linear Grassmann manifold Gr
n
(M) of n–dimensional submanifolds in M. A closed (n+2)–form on M gives rise to a closed 2–form on Gr
n
(M). If the original form was integral, the 2–form will be the curvature of a principal S
1
–bundle over Gr
n
(M). Using this S
1
–bundle one obtains central extensions for certain groups of diffeomorphisms of M. We can realize Gr
m–2
(M) as coadjoint orbits of the extended group of exact volume preserving diffeomorphisms and the symplectic Grassmannians SGr
2k
(M) as coadjoint orbits in the group of Hamiltonian diffeomorphisms.
Mathematics Subject Classification (2000):58B20Both authors are supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austrian Science Fund), project number P14195-MAT 相似文献
3.
Let m and n be nonnegative integers. Denote by P(m,n) the set of all triangle-free graphs G such that for any independent m-subset M and any n-subset N of V(G) with M ∩ N = Ø, there exists a unique vertex of G that is adjacent to each vertex in M and nonadjacent to any vertex in N. We prove that if m ? 2 and n ? 1, then P(m,n) = Ø whenever m ? n, and P(m,n) = {Km,n+1} whenever m > n. We also have P(1,1) = {C5} and P(1,n) = Ø for n ? 2. In the degenerate cases, the class P(0,n) is completely determined, whereas the class P(m,0), which is most interesting, being rich in graphs, is partially determined. 相似文献
4.
Let D(G) be the minimum quantifier depth of a first order sentence Φ that defines a graph G up to isomorphism. Let D0(G) be the version of D(G) where we do not allow quantifier alternations in Φ. Define q0(n) to be the minimum of D0(G) over all graphs G of order n.We prove that for all n we have
log*n−log*log*n−2≤q0(n)≤log*n+22,