- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 17:31:38
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=77&iss=1&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
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
77
2002
1
Pincement de polynômes
Peter
Haïssinsky
Université Paul Sabatier, TOULOUSE CEDEX 9, FRANCE
Ensemble de Julia, déformation quasiconforme, point parabolique, polynôme semi-hyperbolique
Let $ f_{0} : \mathbb{C} \to \mathbb{C} $ be a semi-hyperbolic polynomial in the sense of Carleson-Jones-Yoccoz with an attracting point. The goal of this paper is to show that one can define a semi-hyperbolic deformation $ (f_{t})_{t\ge 0} $ such that the attracting cycle becomes parabolic for the limit polynomial $ f_{\infty} $ and that $ f_{0} $ and $ f_{\infty} $ are semi-conjugate. This deformation is defined by pinching curves in appropriate quotient spaces.
Field theory and polynomials
General
1
23
10.1007/s00014-002-8329-z
http://www.ems-ph.org/doi/10.1007/s00014-002-8329-z
Logarithmic cohomology of the complement of a plane curve
F.
Calderón Moreno
Universidad de Sevilla, SEVILLA, SPAIN
D.
Mond
University of Warwick, COVENTRY, UNITED KINGDOM
Luis
Narváez Macarro
Universidad de Sevilla, SEVILLA, SPAIN
M.
Calderón-Moreno
Universidad de Sevilla, SEVILLA, SPAIN
Algebraic geometry
General
24
38
10.1007/s00014-002-8330-6
http://www.ems-ph.org/doi/10.1007/s00014-002-8330-6
Harmonic forms and near-minimal singular foliations
G.
Katz
, FRAMINGHAM, UNITED STATES
Closed 1-forms, intrinsic harmonicity, minimal foliations, volume-minimizing cycles, Morse-type singularities
For a closed 1-form $ \omega $ with Morse singularities, Calabi discovered a simple global criterion for the existence of a Riemannian metric in which $ \omega $ is harmonic. For a codimension 1 foliation $ \cal {F} $, Sullivan gave a condition for the existence of a Riemannian metric in which all the leaves of $ \cal {F} $ are minimal hypersurfaces. The conditions of Calabi and Sullivan are strikingly similar. If a closed form $ \omega $ has no singularities, then both criteria are satisfied and, for an appropriate choice of metric, $ \omega $ is harmonic and the associated foliation $ \cal {F}_\omega $ is comprised of minimal leaves. However, when $ \omega $ has singularities, the foliation $ \cal {F}_\omega $ is not necessarily minimal.¶ We show that the Calabi condition enables one to find a metric in which $ \omega $ is harmonic and the leaves of the foliation are minimal outside a neighborhood U of the $ \omega $-singular set. In fact, we prove the best possible result of this type: we construct families of metrics in which, as U shrinks to the singular set, the taut geometry of the foliation $ \cal {F}_\omega $ outside U remains stable. Furthermore, all compact leaves missing U are volume minimizing cycles in their homology classes. Their volumes are controlled explicitly.
Manifolds and cell complexes
General
39
77
10.1007/s00014-002-8331-5
http://www.ems-ph.org/doi/10.1007/s00014-002-8331-5
On the Haefliger-Hirsch-Wu invariants for embeddings and immersions
A.
Skopenkov
Moscow State University, MOSCOW, RUSSIAN FEDERATION
Embedding, deleted product, engulfing, singular set, metastable case, isotopy, immersion, smoothing, knotted tori
We prove beyond the metastable dimension the PL cases of the classical theorems due to Haefliger, Harris, Hirsch and Weber on the deleted product criteria for embeddings and immersions. The isotopy and regular homotopy versions of the above theorems are also improved. We show by examples that they cannot be improved further. These results have many interesting corollaries, e.g. 1) Any closed homologically 2-connected smooth 7-manifold smoothly embeds in $ \mathbb{R}^11 $. 2) If $ p \leq q $ and $ m \geq \frac{3q}2 + p + 2 $ then the set of PL embeddings $ S^{p} \times S^{q} \to \mathbb{R}^m $ up to PL isotopy is in 1-1 correspondence with $ \pi_q(V_{m-q,p+1})\oplus\pi_p(V_{m-p,q+1}) $.
Differential geometry
General
78
124
10.1007/s00014-002-8332-4
http://www.ems-ph.org/doi/10.1007/s00014-002-8332-4
Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid
TAKASHI
KAWAMURA
UNIVERSITY OF TOKYO, TOKYO, JAPAN
Unknotting number, four-dimensional clasp number, slice Euler characteristic, Jones polynomial
By means of a result due to Fiedler, we obtain a relation between the lowest degree of the Jones polynomial and the unknotting number for any link which has a closed positive braid diagram. Furthermore, we obtain relations between the lowest degree and the slice euler characteristic or the four-dimensional clasp number.
Group theory and generalizations
General
125
132
10.1007/s00014-002-8333-3
http://www.ems-ph.org/doi/10.1007/s00014-002-8333-3
Quasi-isometries between groups with infinitely many ends
P.
Papasoglu
Université Paris-Sud, ORSAY CX, FRANCE
Kevin
Whyte
University of Illinois at Chicago, CHICAGO, UNITED STATES
Group theory and generalizations
General
133
144
10.1007/s00014-002-8334-2
http://www.ems-ph.org/doi/10.1007/s00014-002-8334-2
GW invariants and invariant quotients
M.
Halic
Ruhr-Universität Bochum, BOCHUM, GERMANY
Gromov-Witten invariants, group actions, Hamiltonian invariants
Given a complex, projective variety and a connected, reductive group acting on it, we investigate the relationship between the Gromov-Witten invariants of the variety and those of its invariant quotient for the group action. Certain so-called Hamiltonian invariants naturally appear in the context.
Global analysis, analysis on manifolds
General
145
191
10.1007/s00014-002-8335-1
http://www.ems-ph.org/doi/10.1007/s00014-002-8335-1
The Huber theorem for non-compact conformally flat manifolds
Gilles
Carron
Université de Nantes, NANTES, FRANCE
Marc
Herzlich
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Manifolds and cell complexes
General
192
220
10.1007/s00014-002-8336-0
http://www.ems-ph.org/doi/10.1007/s00014-002-8336-0