- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:02:30
11
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=LEM&vol=60&iss=1&update_since=2024-03-29
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
60
2014
1
Systole and $\lambda_{2g–2}$ of closed hyperbolic surfaces of genus $g$
Sugata
Mondal
Université Paul Sabatier, TOULOUSE CEDEX 9, FRANCE
Hyperbolic surfaces, eigenfunctions
We apply topological methods to study eigenvalues of the Laplacian on closed hyperbolic surfaces. For any closed hyperbolic surface $S$ of genus $g$, we get a geometric lower bound on ${\lambda_{2g-2}(S)}:$ ${\lambda_{2g-2}(S)} > {1/4} + {\epsilon_0}(S) > 0,$ where ${\epsilon_0}(S)$ is an explicit constant which depends only on the systole of $S$.
Functions of a complex variable
Partial differential equations
3
24
10.4171/LEM/60-1/2-1
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-1
Moduli spaces in genus zero and inversion of power series
Curtis
McMullen
Harvard University, CAMBRIDGE, UNITED STATES
Moduli space, Euler characteristic, stable graphs
This note shows, using elementary properties of ribbon trees, that the universal formula for the inversion of power series can be obtained by counting strata in the compactified moduli space $\cMbar_{0,n}$.
Several complex variables and analytic spaces
25
30
10.4171/LEM/60-1/2-2
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-2
Hyperorthogonal family of vectors and the associated Gram matrix
Bent
Fuglede
University of Copenhagen, COPENHAGEN Ø, DENMARK
Gram matrix, hyperorthogonal, spherical S-code
A family of non-zero vectors in Euclidean $n$-space is termed hyperorthogonal if the angle between any two distinct vectors of the family is at least $\pi /2$. Any hyperorthogonal family is finite and contains at most $2n$ vectors. It decomposes uniquely into the union of mutually orthogonal irreducible subfamilies. An equivalent formulation in terms of the associated Gram matrix is given.
Linear and multilinear algebra; matrix theory
31
41
10.4171/LEM/60-1/2-3
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-3
Crooked halfspaces
Jean-Philippe
Burelle
University of Maryland, COLLEGE PARK, UNITED STATES
Tomasz
Kaszynski
Université de Sherbrooke, SHERBROOKE, CANADA
Todd
Drumm
Howard University, WASHINGTON, UNITED STATES
William
Goldman
University of Maryland, COLLEGE PARK, UNITED STATES
Minkowski space, timelike, spacelike, lightlike, null, particle, photon, crooked plane, crooked halfspace, tachyon, halfplane in the hyperbolic plane
We develop the Lorentzian geometry of a crooked halfspace in (2+1)-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types, giving an explicit slice for the action of the automorphism group. The set of parallelism classes of timelike lines, or particles, in a crooked halfspace is a geodesic halfplane in the hyperbolic plane. Every point in an open crooked halfspace lies on a particle. The correspondence between crooked halfspaces and halfplanes in hyperbolic 2-space preserves the partial order defined by inclusion, and the involution defined by complementarity. We find conditions for when a particle lies completely in a crooked half space. We revisit the disjointness criterion for crooked planes developed by Drumm and Goldman in terms of the semigroup of translations preserving a crooked halfspace. These ideas are then applied to describe foliations of Minkowski space by crooked planes.
Differential geometry
43
78
10.4171/LEM/60-1/2-4
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-4
The virtual fibering theorem for 3-manifolds
Stefan
Friedl
Universität Regensburg, REGENSBURG, GERMANY
Takahiro
Kitayama
Tokyo Institute of Technology, TOKYO, JAPAN
Fibered 3-manifolds, RFRS groups
In 2007 Agol showed that if $N$ is an aspherical compact 3-manifold with empty or toroidal boundary such that $\pi_1(N)$ is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol’s theorem using complexities of sutured manifolds.
Manifolds and cell complexes
79
107
10.4171/LEM/60-1/2-5
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-5
Well-rounded equivariant deformation retracts of Teichmüller spaces
Lizhen
Ji
University of Michigan, ANN ARBOR, UNITED STATES
Teichmüller space, spine, mapping class group, classifying space
In this paper, we construct spines, i.e., $\mathrm {Mod}_g$-equivariant deformation retracts, of the Teichmüller space $\mathcal T_g$ of compact Riemann surfaces of genus $g$. Specifically, we define a $\mathrm {Mod}_g$-stable subspace $S$ of positive codimension and construct an intrinsic $\mathrm {Mod}_g$-equivariant deformation retraction from $mathcal T_g$ to $S$. As an essential part of the proof, we construct a canonical $\mathrm {Mod}_g$-deformation retraction of the Teichmüller space $\mathcal T_g$ to its thick part $\mathcal T_g(\varepsilon)$ when $\varepsilon$ is sufficiently small. These equivariant deformation retracts of $\mathcal T_g$ give cocompact models of the universal space $\underline{E}\mathrm {Mod}_g$ for proper actions of the mapping class group $\mathrm {Mod}_g$. These deformation retractions of $\mathcal T_g$ are motivated by the well-rounded deformation retraction of the space of lattices in $\mathbb R^n$. We also include a summary of results and difficulties of an unpublished paper of Thurston on a potential spine of the Teichmüller space.
Several complex variables and analytic spaces
Topological groups, Lie groups
109
129
10.4171/LEM/60-1/2-6
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-6
On the structure of endomorphisms of projective modules
Daniel
Ferrand
Université Pierre et Marie Curie, PARIS, FRANCE
Dan
Laksov
KTH - Royal Institute of Technology, STOCKHOLM, SWEDEN
Projective modules, characteristic polynomials, eigenspaces, étale algebras, Jordan decomposition
Taking as a model the completed theory of vector space endomorphisms, the present text aims at extending this theory to endomorphisms of finitely generated projective modules over a general commutative ring; now analogous results often require totally different methods of proof. The first important result is a structure theorem for such modules when the characteristic polynomial of the endomorphism is separable. The second topic deals with the minimal polynomial, whose mere existence is shown to require additional hypotheses, even over a domain. In the third topic we extend the classical notion of ‘cyclic modules’ as the modules which are invertible over the ring of polynomials modulo the characteristic polynomial. Regarding the diagonalization of endomorphisms, we show that a classical criterion of being diagonalizable over some extension of the base field can be transferred nearly verbatim to rings, provided that diagonalization is expected only after some faithfully flat base change. Many results that hold over a field, like the fact that commuting diagonalizable endomorphisms are simultaneously diagonalizable, hold over arbitrary rings, with this extended meaning of diagonalization. The Jordan-Chevalley-Dunford decomposition, shown as a particular case of the lifting property of étale algebras, also holds over rings. Finally, in several reasonable situations, the eigenspace associated with any root of the characteristic polynomial is shown to be given a more concrete description as the image of a map. In these situations the classical theory generalizes to rings.
Commutative rings and algebras
Algebraic geometry
Linear and multilinear algebra; matrix theory
131
175
10.4171/LEM/60-1/2-7
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-7
Alternative invariants for the embedded resolution of purely inseparable surface singularities
Herwig
Hauser
Universität Innsbruck, INNSBRUCK, AUSTRIA
Dominique
Wagner
Universität Innsbruck, INNSBRUCK, AUSTRIA
Surfaces, resolution, singularities, positive characteristic, blowups
We propose two local invariants for the inductive proof of the embedded resolution of purely inseparable surface singularities of order equal to the characteristic. The invariants are built on a detailed analysis of the so called “kangaroo phenomenon” in positive characteristic. They thus measure accurately the algebraic complexity of an equation defining a surface singularity in characteristic $p$. As the invariants are shown to drop after each blowup, induction applies.
Algebraic geometry
Commutative rings and algebras
Several complex variables and analytic spaces
177
224
10.4171/LEM/60-1/2-8
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-8
Commission Internationale de l'Enseignement Mathématique. The Klein Project
General
225
226
10.4171/LEM/60-1/2-9
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-9
Commission Internationale de l'Enseignement Mathématique. Discussion Document for the Twenty-third ICMI Study. Primary mathematics Study on whole numbers
General
227
230
10.4171/LEM/60-1/2-10
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-10
Bulletin bibliographique
General
0
0
10.4171/LEM/60-1/2-11
http://www.ems-ph.org/doi/10.4171/LEM/60-1/2-11