- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 13:07:29
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=73&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
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
73
1998
4
$\pi_1$-injective surfaces in graph manifolds
J. Hyam
Rubinstein
University of Melbourne, PARKVILLE, VIC, AUSTRALIA
Shicheng
Wang
Peking University, BEIJING, CHINA
Manifolds and cell complexes
General
499
515
10.1007/s000140050066
http://www.ems-ph.org/doi/10.1007/s000140050066
Minimal orbits close to periodic frequencies
U.
Bessi
Scuola Normale Superiore, PISA, ITALY
V.
Semijopuva
Scuola Normale Superiore, PISA, ITALY
Quasi-integrable Hamiltonian systems, Anbry-Mather theory, Arnold's diffusion
Let ${\cal L}(Q,\dot Q)={1\over2}\vert\dot{Q}\vert^2+h(Q,\dot Q)$ with h analytic of small norm. The problem of Arnold's diffusion consists in finding conditions on h which guarantee the existence of orbits Q of ${\cal L}$ with $\dot Q$ connecting two arbitrary points of frequency space. Recently, J. N. Mather has found a sufficient condition for Arnold's diffusion; this condition is not read on h itself, but on the set of all action-minimizing orbits of ${\cal L}$. In this paper we try to characterize those action-minimizing orbits whose mean frequency is close to periodic.
Calculus of variations and optimal control; optimization
General
516
547
10.1007/s000140050067
http://www.ems-ph.org/doi/10.1007/s000140050067
S.A.G.B.I. bases for rings of formal modular seminvariants
R.
Shank
Queen's University, KINGSTON, ONTARIO, CANADA
Invariant theory, Indecomposable modular representation
We use the theory of S.A.G.B.I. bases to construct a generating set for the ring of invariants for the four and five dimensional indecomposable modular representations of a cyclic group of prime order. We observe that for the four dimensional representation the ring of invariants is generated in degrees less than or equal to 2p-3, and for the five dimensional representation the ring of invariants is generated in degrees less than or equal to 2p-2.
Group theory and generalizations
General
548
565
10.1007/s000140050068
http://www.ems-ph.org/doi/10.1007/s000140050068
Fano contact manifolds and nilpotent orbits
Ting-Yu
Lee
Ecole Normale Superieure, PARIS CEDEX 05, FRANCE
Contact structure, Fano manifolds, quaternion-Kähler manifolds, nilpotent orbits, contact moment map
A contact structure on a complex manifold M is a corank 1 subbundle F of TM such that the bilinear form on F with values in the quotient line bundle L = TM/F deduced from the Lie bracket of vector fields is everywhere non-degenerate. In this paper we consider the case where M is a Fano manifold; this implies that L is ample. If ${\frak g}$ is a simple Lie algebra, the unique closed orbit in ${\bold P}({\frak g})$ (for the adjoint action) is a Fano contact manifold; it is conjectured that every Fano contact manifold is obtained in this way. A positive answer would imply an analogous result for compact quaternion-Kahler manifolds with positive scalar curvature, a longstanding question in Riemannian geometry. In this paper we solve the conjecture under the additional assumptions that the group of contact automorphisms of M is reductive, and that the image of the rational map M$--\rightarrow$ P(H0(M, L)*) sociated to L has maximum dimension. The proof relies on the properties of the nilpotent orbits in a semi-simple Lie algebra, in particular on the work of R. Brylinski and B. Kostant.
Global analysis, analysis on manifolds
General
566
583
10.1007/s000140050069
http://www.ems-ph.org/doi/10.1007/s000140050069
Stable constant mean curvature hypersurfaces in some Riemannian manifolds
S.
Montiel
Universidad de Granada, GRANADA, SPAIN
Constant mean curvature, hypersurface, stability
We determine all stable constant mean curvature hypersurfaces in a wide class of complete Riemannian manifolds having a foliation whose leaves are umbilical hypersurfaces. Among the consequences of this analysis we obtain all the stable constant mean curvature hypersurfaces in many nonsimply connected hyperbolic space forms.
Manifolds and cell complexes
General
584
602
10.1007/s000140050070
http://www.ems-ph.org/doi/10.1007/s000140050070
Schubert polynomials and Bott-Samelson varieties
Peter
Magyar
Michigan State University, EAST LANSING, UNITED STATES
Flag variety, Young tableaux, Demazure character formula
Schubert polynomials generalize Schur polynomials, but it is not clear how to generalize several classical formulas: the Weyl character formula, the Demazure character formula, and the generating series of semistandard tableaux. We produce these missing formulas and obtain several surprising expressions for Schubert polynomials. The above results arise naturally from a new geometric model of Schubert polynomials in terms of Bott-Samelson varieties. Our analysis includes a new, explicit construction for a Bott-Samelson variety Z as the closure of a B-orbit in a product of flag varieties. This construction works for an arbitrary reductive group G, and for G = GL(n) it realizes Z as the representations of a certain partially ordered set. This poset unifies several well-known combinatorial structures: generalized Young diagrams with their associated Schur modules; reduced decompositions of permutations; and the chamber sets of Berenstein-Fomin-Zelevinsky, which are crucial in the combinatorics of canonical bases and matrix factorizations. On the other hand, our embedding of Z gives an elementary construction of its coordinate ring, and allows us to specify a basis indexed by tableaux.
Group theory and generalizations
General
603
636
10.1007/s000140050071
http://www.ems-ph.org/doi/10.1007/s000140050071
Cogroups in algebras over an operad are free algebras
B.
Fresse
Université de Nice, NICE CEDEX 2, FRANCE
Cogroup, operad
Let $\cal P$ be an operad defined over a field of characteristic zero. Let R be a cogroup in the category of complete ${\cal P}$-algebras. In this article, we show that R is necessarily the completion of a free ${\cal P}$-algebra. We also handle the case of cogroups in connected graded algebras over an operad, and the case of groups in connected graded coalgebras over an operad.
Category theory; homological algebra
General
637
676
10.1007/s000140050072
http://www.ems-ph.org/doi/10.1007/s000140050072