- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 20:48:57
18
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=LEM&vol=55&update_since=2024-03-28
L’Enseignement Mathématique
Enseign. Math.
LEM
0013-8584
2309-4672
General
10.4171/LEM
http://www.ems-ph.org/doi/10.4171/LEM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Fondation L’Enseignement Mathématique
55
2009
1
Finiteness and constructibility in local analytic geometry
Mauricio
Garay
, BURES-SUR-YVETTE, FRANCE
Using the Houzel finiteness theorem and the Whitney-Thom stratification theory we show, in local analytic geometry, that relatively constructible sheaves have coherent higher direct images.
General
3
31
10.4171/LEM/55-1-1
http://www.ems-ph.org/doi/10.4171/LEM/55-1-1
On the quantization of conjugacy classes
Eckhard
Meinrenken
University of Toronto, TORONTO, ONTARIO, CANADA
Let $G$ be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level $k\ge 0$ fusion ring $R_k(G)$ of $G$ with the twisted equivariant $K$-homology at level $k+h^v$, where $h^v$ is the dual Coxeter number of $G$. In this paper, we will review this result using the language of Dixmier-Douady bundles. We show that the additive generators of the group $R_k(G)$ are obtained as $K$-homology push-forwards of the fundamental classes of pre-quantized conjugacy classes in $G$.
General
33
75
10.4171/LEM/55-1-2
http://www.ems-ph.org/doi/10.4171/LEM/55-1-2
The Planar Rook Algebra and Pascal's Triangle
Daniel
Flath
Macalester College, SAINT PAUL, UNITED STATES
Tom
Halverson
Macalester College, SAINT PAUL, UNITED STATES
Kathryn
Herbig
, , UNITED STATES
General
77
92
10.4171/LEM/55-1-3
http://www.ems-ph.org/doi/10.4171/LEM/55-1-3
A contact geometric proof of the Whitney-Graustein theorem
Hansjörg
Geiges
Universiteit Leiden, LEIDEN, NETHERLANDS
The Whitney–Graustein theorem states that regular closed curves in the $2$-plane are classified, up to regular homotopy, by their rotation number. Here we give a simple proof based on contact geometry.
General
93
102
10.4171/LEM/55-1-4
http://www.ems-ph.org/doi/10.4171/LEM/55-1-4
Capture pursuit games on unbounded domains
S.
Alexander
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
R.
Bishop
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Robert
Ghrist
University of Illinois, URBANA, UNITED STATES
We introduce simple tools from geometric convexity to analyze capture-type (or "Lion and Man'') pursuit problems in unbounded domains. The main result is a necessary and sufficient condition for eventual capture in equal-speed discrete-time multi-pursuer capture games on convex Euclidean domains of arbitrary dimension and shape. This condition is presented in terms of recession sets in unit tangent spheres. The chief difficulties lie in utilizing the boundary of the domain as a constraint on the evader's escape route. We also show that these convex-geometric techniques provide sufficient criteria for pursuit problems in non-convex domains with a convex decomposition.
General
103
125
10.4171/LEM/55-1-5
http://www.ems-ph.org/doi/10.4171/LEM/55-1-5
The Big Picard Theorem and other results on Riemann surfaces
Pablo
Arés-Gastesi
Tata Institute of Fundamental Research, MUMBAI, INDIA
Tyakal Nanjundiah
Venkataramana
Tata Institute of Fundamental Research, MUMBAI, INDIA
In this paper we provide a new proof of the Big Picard Theorem, based on some simple observations about mappings between Riemann surfaces.
General
127
137
10.4171/LEM/55-1-6
http://www.ems-ph.org/doi/10.4171/LEM/55-1-6
Ternary cubic forms and Etale algebras
Melanie
Raczek
Université Catholique de Louvain, LOUVAIN-LA NEUVE, BELGIUM
Jean-Pierre
Tignol
Université Catholique de Louvain, LOUVAIN-LA NEUVE, BELGIUM
General
139
156
10.4171/LEM/55-1-7
http://www.ems-ph.org/doi/10.4171/LEM/55-1-7
$G_2$ and the rolling distribution
Gil
Bor
CIMAT, GUANAJUATO - GTO, MEXICO
Richard
Montgomery
University of California at Santa Cruz, SANTA CRUZ, UNITED STATES
General
157
196
10.4171/LEM/55-1-8
http://www.ems-ph.org/doi/10.4171/LEM/55-1-8
Commission Internationale de l'Enseignement Mathématique. Discussion Document for the Twentieth ICMI Study
General
197
209
10.4171/LEM/55-1-9
http://www.ems-ph.org/doi/10.4171/LEM/55-1-9
3
Elliptic Dedekind Domains Revisited
Pete
Clark
University of Georgia, ATHENS, UNITED STATES
We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain $R$. We can choose $R$ to be the integral closure of a PID in a quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green.
General
213
225
10.4171/LEM/55-3-1
http://www.ems-ph.org/doi/10.4171/LEM/55-3-1
Sur les feuilletages de l'espace projectif ayant une composante de Kupka
Marco
Brunella
Université de Bourgogne, DIJON CEDEX, FRANCE
General
227
234
10.4171/LEM/55-3-2
http://www.ems-ph.org/doi/10.4171/LEM/55-3-2
The Hesse pencil of plane cubic curves
Michela
Artebani
Universidad de Concepción, CONCEPCION, CHILE
Igor
Dolgachev
University of Michigan, ANN ARBOR, UNITED STATES
This is a survey of the classical geometry of the Hesse configuration of 12 lines in the projective plane with relation to the inflection points of a plane cubic curve. We also study two $K3$ surfaces with Picard number 20 which arise naturally in connection with this configuration.
General
235
273
10.4171/LEM/55-3-3
http://www.ems-ph.org/doi/10.4171/LEM/55-3-3
On the Danilov-Gizatullin Isomorphism Theorem
Hubert
Flenner
Ruhr-Universität Bochum, BOCHUM, GERMANY
Shulim
Kaliman
University of Miami, CORAL GABLES, UNITED STATES
Mikhail
Zaidenberg
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
A {\it Danilov-Gizatullin surface} is a normal affine surface $V=\Sigma_d\setminus S$, which is a complement to an ample section $S$ in a Hirzebruch surface $\Sigma_d$. By a surprising result due to Danilov and Gizatullin [DaGi], $V$ depends only on $n=S^2$ and neither on $d$ nor on $S$. In this note we provide a new and simple proof of this Isomorphism Theorem.
General
275
283
10.4171/LEM/55-3-4
http://www.ems-ph.org/doi/10.4171/LEM/55-3-4
Sur la linéarisation des tissus
Luc
Pirio
Université de Rennes 1, RENNES CEDEX, FRANCE
Nous présentons un critère analytique simple qui caractérise les tissus en hypersurfaces linéarisables. Nous en donnons une interprétation géométrique invariante en termes de connexion projective. Nous expliquons que notre approche permet de traiter le problème de la linéarisation d'objets plus généraux que les tissus de codimension~1. Quelques exemples particuliers sont ensuite étudiés en guise d'illustration. Nous terminons par des remarques historiques sur la question abordée ici.
General
285
328
10.4171/LEM/55-3-5
http://www.ems-ph.org/doi/10.4171/LEM/55-3-5
On a theorem of René Thom in Géométrie Finie
Marc
Chaperon
Université Paris 7, PARIS CEDEX 13, FRANCE
Daniel
Meyer
Université Paris 7, PARIS CEDEX 13, FRANCE
We study generalisations of the following fact: a generic compact curve in the plane intersects every straight line in a finite number of points; moreover, for each such curve, this number is bounded. Our results develop the first part of René Thom's 1968 paper on Géométrie finie ("finite geometry'').
General
329
357
10.4171/LEM/55-3-6
http://www.ems-ph.org/doi/10.4171/LEM/55-3-6
On the Cauchy-Kowalevski Theorem
Marc
Chaperon
Université Paris 7, PARIS CEDEX 13, FRANCE
After a short review of the basic properties of analytic functions, we apply the infinite-dimensional theory to get a simple proof of the Cauchy-Kowalevski theorem, in an infinite-dimensional version which seems to be new.
General
359
371
10.4171/LEM/55-3-7
http://www.ems-ph.org/doi/10.4171/LEM/55-3-7
Cohomology of Lie $2$-groups
Grégory
Ginot
Université Pierre et Marie Curie, PARIS, FRANCE
Ping
Xu
University of Luxembourg, LUXEMBOURG, LUXEMBOURG
We study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module $A \to 1$. The cohomology of the Lie 2-groups corresponding to the universal crossed modules $G\to \mathrm {Aut}(G)$ and $G\to \mathrm {Aut}^+(G)$ is the abutment of a spectral sequence involving the cohomology of $GL(n,\mathbb Z)$ and $SL(n,\mathbb Z)$. When the dimension of the center of $G$ is less than 3, we compute these cohomology groups explicitly. We also compute the cohomology of the Lie 2-group corresponding to a crossed module $G{\xrightarrow[i]} H$ for which $\ker(i)$ is compact and Coker$(i)$ is connected, simply connected and compact, and we apply the result to the {\it string} 2-group.
General
373
396
10.4171/LEM/55-3-8
http://www.ems-ph.org/doi/10.4171/LEM/55-3-8
Commission Internationale de l'Enseignement Mathématique. Looking back to the Future of the Teaching and Learning of Algebra
Kaye
Stacey
University of Melbourne, MELBOURNE, VICTORIA, AUSTRALIA
General
397
402
10.4171/LEM/55-3-9
http://www.ems-ph.org/doi/10.4171/LEM/55-3-9