- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 11:14:30
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=72&iss=3&update_since=2024-03-28
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
72
1997
3
The asymptotic behavior of the set of rays
S.
Mendonça
Universidade Federal Fluminense - UFF, NITERÓI - RJ, BRAZIL
Ideal boundary, set of rays
We introduce new invariants to study the asymptotic behavior of the set of rays and prove a splitting theorem for the radius of the ideal boundary of an open manifold with $ K \ge 0 $ (Shioya's Conjecture).
Global analysis, analysis on manifolds
General
331
348
10.1007/s000140050021
http://www.ems-ph.org/doi/10.1007/s000140050021
On the rigidity of discrete isometry groups of negatively curved spaces
Sa'ar
Hersonsky
University of Georgia, ATHENS, UNITED STATES
Frédéric
Paulin
Ecole Normale Superieure, PARIS CEDEX 05, FRANCE
Manifolds and cell complexes
General
349
388
10.1007/s000140050022
http://www.ems-ph.org/doi/10.1007/s000140050022
Picard groups of multiplicative invariants
Martin
Lorenz
Temple University, PHILADELPHIA, UNITED STATES
Picard group, ring of invariants, group action, Grothendieck group, polycyclic group algebra, Cartan map, class group, 1-cohomology group
Let S = kA denote the group algebra of a finitely generated free abelian group A over the field k and let G be a finite subgroup of GL(A). Then G acts on S by means of the unique extension of the natural GL(A)-action on A. We determine the Picard group Pic R of the algebra of invariants R = SG. As an application, we produce new polycyclic group algebras with nontrivial torsion in K0.
Group theory and generalizations
General
389
399
10.1007/s000140050023
http://www.ems-ph.org/doi/10.1007/s000140050023
On foliated circle bundles over closed orientable 3-manifolds
Shigeaki
Miyoshi
Chuo University, TOKYO, JAPAN
Foliated circle bundles, Milnor-Wood inequality, Fuchsian groups
We show that there exists a family of smooth orientable circle bundles over closed orientable 3-manifolds each of which has a codimension-one foliation transverse to the fibres of class C0 but has none of class C3. There arises a necessary condition induced from the Milnor-Wood inequality for the existence of a foliation transverse to the fibres of an orientable circle bundle over a closed orientable 3-manifold. We show that with some exceptions this necessary condition is also sufficient for the existence of a smooth transverse foliation if the base space is a closed Seifert fibred manifold.
Manifolds and cell complexes
General
400
410
10.1007/s000140050024
http://www.ems-ph.org/doi/10.1007/s000140050024
Sur les feuilletages algébriques de Rolle
F.
Chazal
Université de Bourgogne, DIJON CEDEX, FRANCE
Algebraic set, fibration, Pfaffian hypersurface, polynomial, real algebraic foliation, separatrix, space of leaves
L'objet de ce travail est l'étude des feuilletages algébriques de Rolle dans $ \Bbb {R}^n $. On montre que leur restriction au complémentaire d'un nombre fini de feuilles possède une structure de produit. On précise aussi la topologie de certaines de leurs feuilles.
Algebraic geometry
General
411
425
10.1007/s000140050025
http://www.ems-ph.org/doi/10.1007/s000140050025
Differential operators commuting with invariant functions
T.
Levasseur
Université de Brest, BREST CEDEX 3, FRANCE
J. Toby
Stafford
The University of Manchester, MANCHESTER, UNITED KINGDOM
Algebraic geometry
General
426
433
10.1007/s000140050026
http://www.ems-ph.org/doi/10.1007/s000140050026
Gabriel filters in real closed rings
Niels
Schwartz
Universität Passau, PASSAU, GERMANY
f -ring, real closed ring, valuation ring, Gabriel filter, Gabriel localization, ring of quotiens, prime ideal, scheme, ring of sections, real spectrum
Real closed rings arise in semi-algebraic geometry and topology as well as in the investigation of partially ordered rings. It is shown that localizations of real closed rings with respect to Gabriel filters, or more generally: multiplicative filters, are again real closed. Thus, real closedness is preserved under a large number of important ring theoretic constructions. For a few particularly simple cases the multiplicative filters are classified and the localizations are determined.
Commutative rings and algebras
General
434
465
10.1007/s000140050027
http://www.ems-ph.org/doi/10.1007/s000140050027
Topology of complete intersections
F.
Fang
NANKAI UNIVERSITY, TIANJIN, CHINA
Complete intersection, homotopy equivalence, homeomorphism
Let Xn(d) and Xn(d') be two n-dimensional complete intersections with the same total degree d. In this paper we prove that, if n is even and d has no prime factors less than $ {n+3}\over{2} $, then Xn(d) and Xn(d') are homotopy equivalent if and only if they have the same Euler characteristics and signatures. This confirms a conjecture of Libgober and Wood [16]. Furthermore, we prove that, if d has no prime factors less than $ {n+3}\over{2} $, then Xn(d) and Xn(d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.
Algebraic geometry
General
466
480
10.1007/s000140050028
http://www.ems-ph.org/doi/10.1007/s000140050028
Critical values of autonomous Lagrangian systems
G.
Paternain
Facultad de Ciencias, MONTEVIDEO, URUGUAY
M.
Paternain
Facultad de Ciencias, MONTEVIDEO, URUGUAY
Lagrangian systems, minimizing measures, critical values
Let M be a closed manifold and $ L : TM \rightarrow \bf {R} $ a convex superlinear Lagrangian. We consider critical values of Lagrangians as defined by R. Mañé in [5]. Let cu(L) denote the critical value of the lift of L to the universal covering of M and let ca(L) denote the critical value of the lift of L to the abelian covering of M. It is easy to see that in general, $ c_{u}(L) \leq c_{a}(L) $. Let c0(L) denote the strict critical value of L defined as the smallest critical value of $ L - \omega $ where $ \omega $ ranges among all possible closed 1-forms. We show that ca(L) = c0(L). We also show that if there exists k such that the Euler-Lagrange flow of L on the energy level k' is Anosov for all $ k'\geq k $, then $ k > c_{u}(L) $. Afterwards, we exhibit a Lagrangian on a compact surface of genus two which possesses Anosov energy levels with energy $ k < c_{a}(L) $, thus answering in the negative a question raised by Mañé. This example also shows that the inequality $ c_{u}(L) \leq c_{a}(L) $ could be strict. Moreover, by a result of M.J. Dias Carneiro [4] these Anosov energy levels do not have minimizing measures. Finally, we describe a large class of Lagrangians for which cu(L) is strictly bigger than the maximum of the energy restricted to the zero section of TM.
Partial differential equations
General
481
499
10.1007/s000140050029
http://www.ems-ph.org/doi/10.1007/s000140050029