- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 03:07:06
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=76&iss=4&update_since=2024-03-29
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
76
2001
4
Transitively twisted flows of 3-manifolds
H.
NAKAYAMA
HIROSHIMA UNIVERSITY, HIGASHI-HIROSHIMA, JAPAN
Angular flow, transitive, minimal, almost periodic
A non-singular C1 vector field X of a closed 3-manifold M generating a flow $ \varphi_t $ induces a flow of the bundle N X orthogonal to X. This flow further induces a flow $ P \varphi_t $ of the projectivized bundle of N X. In this paper, we assume that the projectivized bundle is a trivial bundle, and study the lift $ \angle\varphi_t $ of $ P \varphi_t $ to the infinite cyclic covering $ M \times \mathbb{R}$. We prove that the flow $ \angle\varphi_t $ is not minimal, and construct an example of $ \varphi_t $ such that $ \angle\varphi_t $ has a dense orbit. If $ \varphi_t $ is almost periodic and minimal, then $ \angle\varphi_t $ is shown to be classified into three cases: (1) All the orbits of $ \angle\varphi_t $ are bounded. (2) All the orbits of $ \angle\varphi_t $ are proper. (3) $ \angle\varphi_t $ is transitive.
Manifolds and cell complexes
General
577
588
10.1007/s00014-001-8321-z
http://www.ems-ph.org/doi/10.1007/s00014-001-8321-z
Embedding and knotting of flat compact surfaces in 3-space
Peter
Røgen
Technical University of Denmark, LYNGBY, DENMARK
isotopy classes of flat compact surfaces in 3-space, developable surfaces, Seifert surfaces
In 3-space, any compact surface with nonempty boundary is isotopic to a flat (zero Gaussian curvature) surface and two such flat surfaces are isotopic through flat surfaces if and only if they are isotopic through ordinary surfaces. Hereby the isotopy classes of flat surfaces are in one-to-one correspondence with the isotopy classes of ordinary surfaces which have no constraint in their curvature. Applied to Seifert surfaces we get: Any simple closed space curve can be deformed until it bounds a flat orientable surface.
Global analysis, analysis on manifolds
Differential geometry
General
589
606
10.1007/s00014-001-0000-6
http://www.ems-ph.org/doi/10.1007/s00014-001-0000-6
Relèvements des algèbres lisses et de leurs morphismes
A.
Arabia
Université Paris 7, PARIS CEDEX 05, FRANCE
Smooth algebra, very smooth algebra, Monsky-Washnitzer cohomology
Let R be a commutative ring and let I be any ideal of R, put $ {\bf\it\bar R} : = {\bf\it R} / {\bf\it I} $. We prove that for any smooth $ \bf\it\bar R $-algebra $ \bf\it\bar A $ there exist a smooth R-algebra A such that $ \bf\it\bar A $ is isomorphic to $ {\bf\it\bar R} \otimes_{\bf\it R} {\bf\it A} $. We also show that for any morphism of smooth $ \bf\it\bar R $-algebras $ {\it\bar a} : {\bf\it\bar A} \rightarrow {\bf\it\bar B} $, there exist a morphism of smooth R-algebras $ {\it a} : {\bf\it A} \rightarrow {\bf\it B} $ such that $ {\bf 1} \otimes {\it a} : {\bf\it\bar R} \otimes {\bf\it A} \rightarrow {\bf\it\bar R} \otimes {\bf\it B} $ is isomorphic to $ {\it\bar a} : {\bf\it\bar A} \rightarrow {\bf\it\bar B} $. As a corollary, when R is nmtherian, we show that for any smooth $ \bf\it\bar R $-algebra $ \bf\it\bar A $ there exist a very smooth weakly complete algebra $ {\bf\it A}^\dagger $ over R such that $ {\bf\it\bar R} \otimes {\bf\it A}^\dagger $ is isomorphic to $ \bf\it\bar A $. Soient R un anneau commutatif et I un idéal de R, notons $ {\bf\it\bar R} : = {\bf\it R} / {\bf\it I} $. Nous prouvons que pour toute $ \bf\it\bar R $-algèbre lisse $ \bf\it\bar A $, il existe une R-algèbre lisse A telle que $ \bf\it\bar A $ est isomorphe à $ {\bf\it\bar R} \otimes_{\bf\it R} {\bf\it A} $. Nous prouvons également que pour tout morphisme de $ \bf\it\bar R $-algèbres lisses $ {\it\bar a} : {\bf\it\bar A} \rightarrow {\bf\it\bar B} $, il existe un morphisme de R-algèbres lisses $ {\it a} : {\bf\it A} \rightarrow {\bf\it B} $ tel que $ {\bf 1} \otimes {\it a} : {\bf\it\bar R} \otimes {\bf\it A} \rightarrow {\bf\it\bar R} \otimes {\bf\it B} $ est isomorphe à $ {\it\bar a} : {\bf\it\bar A} \rightarrow {\bf\it\bar B} $. On en déduit, lorsque R est nmthérien, que pour toute $ \bf\it\bar R $-algèbre lisse $ \bf\it\bar A $, il existe une R-algèbre faiblement complète très lisse $ {\bf\it A}^\dagger $ telle que $ {\bf\it\bar R} \otimes {\bf\it A}^\dagger $ est isomorphe à $ \bf\it\bar A $.
Commutative rings and algebras
General
607
639
10.1007/s00014-001-8322-y
http://www.ems-ph.org/doi/10.1007/s00014-001-8322-y
Surfaces de la classe $ \mathrm{VII_{0}} $ admettant un champ de vecteurs, II
G.
Dloussky
CMI-Université d'Aix-Marseille I, MARSEILLE CEDEX 13, FRANCE
K.
Oeljeklaus
CMI-Université d'Aix-Marseille I, MARSEILLE CEDEX 13, FRANCE
M.
Toma
Universität Osnabrück, OSNABRÜCK, GERMANY
Manifolds and cell complexes
General
640
664
10.1007/s00014-001-8323-x
http://www.ems-ph.org/doi/10.1007/s00014-001-8323-x
Localisation des résidus de Baum-Bott, courbes généralisées et K-théorie (I: feuilletages dans $ {\Bbb C}^2 $)
V.
Cavalier
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
D.
Lehmann
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Algebraic topology
General
665
683
10.1007/s00014-001-8324-9
http://www.ems-ph.org/doi/10.1007/s00014-001-8324-9
The Rost invariant has trivial kernel for quasi-split groups of low rank
R.
Garibaldi
UCLA, LOS ANGELES, UNITED STATES
Rost invariant, exceptional groups
For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map $ R_G : H^1(F, G) \rightarrow H^3(F, \mathbb{Q} / \mathbb{Z}(2)) $. This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for exceptional Jordan algebras as special cases. We show that RG has trivial kernel if G is quasi-split of type E6 or E7. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank.
Group theory and generalizations
General
684
711
10.1007/s00014-001-8325-8
http://www.ems-ph.org/doi/10.1007/s00014-001-8325-8
Symplectic topology on subcritical manifolds
Paul
Biran
ETH Zürich, ZÜRICH, SWITZERLAND
Kai
Cieliebak
Universität Augsburg, AUGSBURG, GERMANY
Global analysis, analysis on manifolds
General
712
753
10.1007/s00014-001-8326-7
http://www.ems-ph.org/doi/10.1007/s00014-001-8326-7
Invariant measure and Lyapunov exponents for birational maps of P^2
Jeffrey
Diller
University of Notre Dame, NOTRE DAME, UNITED STATES
Holomorphic dynamics, birational maps, Lyapunov exponents, invariant measures
In this paper we construct and study a natural invariant measure for a birational self-map of the complex projective plane. Our main hypothesis - that the birational map be "separating" - is a condition on the indeterminacy set of the map. We prove that the measure is mixing and that it has distinct Lyapunov exponents. Under a further hypothesis on the indeterminacy set we show that the measure is hyperbolic in the sense of Pesin theory. In this case, we also prove that saddle periodic points are dense in the support of the measure.
Measure and integration
General
754
780
10.1007/s00014-001-8327-6
http://www.ems-ph.org/doi/10.1007/s00014-001-8327-6
Complexity of degenerations of modules
R.
Aehle
Universität Bern, BERN, SWITZERLAND
Christine
Riedtmann
Universität Bern, BERN, SWITZERLAND
Grzegorz
Zwara
Nicolaus Copernicus University, TORUŃ, POLAND
Associative rings and algebras
General
781
803
10.1007/s00014-001-8328-5
http://www.ems-ph.org/doi/10.1007/s00014-001-8328-5