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241.
We present an abstract, yet rather natural concept of automaticity which is based on semigroup
actions. The standard notion of k-automaticity as well as many,
if not all of its generalizations are recovered by specifying appropriate semigroup actions on
$ \mathbb{N}_0 $ or $ \mathbb{N}^N_0 $ or other similar objects—e.g., the standard notion of
k-automaticity is recovered by considering a certain
"natural" action of the free semigroup with k generators on
$ \mathbb{N}_0 $. We show that the main results characterizing automatic sequences (Cobham, 1972,
Math. Systems Theory 6) hold almost verbatim in the general context, too.AMS Subject Classification: 11B85, 68Q45, 16W22, 18DXX. 相似文献
242.
Greg Hjorth 《Journal of the American Mathematical Society》2001,14(1):125-143
Let be a Polish group. We characterize when there is a Polish space with a continuous -action and an analytic set (that is, the Borel image of some Borel set in some Polish space) having uncountably many orbits but no perfect set of orbit inequivalent points.
Such a Polish -space and analytic exist exactly when there is a continuous, surjective homomorphism from a closed subgroup of onto the infinite symmetric group, , consisting of all permutations of equipped with the topology of pointwise convergence.
243.
Jiang Renfang 《数学学报(英文版)》1996,12(1):49-53
The equivalence among bounded homeomorphisms of a surface, reducible homeomorphisms of the surface, bounded automorphisms of the surface group, induced or exchange automorphisms of the surface group, and the stabilizer of the translation length function of the tree action is established. 相似文献
244.
We state and prove the theorem of existence and uniqueness of solutions to ordinary superdifferential equations on supermanifolds. It is shown that any supervector field, X = X0 + X1, has a unique integral flow, Г:
1¦1 x (M, AM) → (M, AM), satisfying a given initial condition. A necessary and sufficient condition for this integral flow to yield an
1¦1-action is obtained: the homogeneous components, X0, and, X1, of the given field must define a Lie superalgebra of dimension (1, 1). The supergroup structure on
1¦1, however, has to be specified: there are three non-isomorphic Lie supergroup structures on
1¦1, all of which have addition as the group operation in the underlying Lie group
. On the other extreme, even if X0, and X1 do not close to form a Lie superalgebra, the integral flow of X is uniquely determined and is independent of the Lie supergroup structure imposed on
1¦1. This fact makes it possible to establish an unambiguous relationship between the algebraic Lie derivative of supergeometric objects (e.g., superforms), and its geometrical definition in terms of integral flows. It is shown by means of examples that if a supergroup structure in
1¦1 is fixed, some flows obtained from left-invariant supervector fields on Lie supergroups may fail to define an
1¦1-action of the chosen structure. Finally, necessary and sufficient conditions for the integral flows of two supervector fields to commute are given. 相似文献
245.
Andrea Spiro 《Proceedings of the American Mathematical Society》2000,128(4):1141-1145
Let be a compact homogeneous manifold with acting effectively and with a -invariant CR structure of hypersurface type; then any maximal compact subgroup acts transitively on .
246.
David Harbater Leila Schneps 《Transactions of the American Mathematical Society》2000,352(7):3117-3148
Let denote the moduli space of Riemann spheres with ordered marked points. In this article we define the group of quasi-special symmetric outer automorphisms of the algebraic fundamental group for all to be the group of outer automorphisms respecting the conjugacy classes of the inertia subgroups of and commuting with the group of outer automorphisms of obtained by permuting the marked points. Our main result states that is isomorphic to the Grothendieck-Teichmüller group for all .
247.
Christine M. Escher Shari K. Ultman 《Topology and its Applications》2011,158(1):38-51
In light of recent advances in the study of manifolds admitting Riemannian metrics of positive sectional curvature, the study of certain infinite families of seven dimensional manifolds has become a matter of interest. We determine the cohomology ring structures of manifolds belonging to these families. This particular ring structure indicates the existence of topological invariants distinguishing the corresponding homeomorphism and diffeomorphism type. We show that all families contain representatives of infinitely many homotopy types. 相似文献
248.
249.