Journal für die reine und angewandte Mathematik

Published by De Gruyter

Volume 2012 Issue 669

Issue of Journal für die reine und angewandte Mathematik

Contents
Journal Overview

September 20, 2011

String topology of classifying spaces

David Chataur, Luc Menichi

Page range: 1-45

Abstract

Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let ℒ BG ≔ map( S 1 , BG ) be the free loop space of BG , i.e. the space of continuous maps from the circle S 1 to BG . The purpose of this paper is to study the singular homology H * (ℒ BG ) of this loop space. We prove that when taken with coefficients in a field the homology of ℒ BG is a homological conformal field theory. As a byproduct of our Main Theorem, we get a Batalin–Vilkovisky algebra structure on the cohomology H * (ℒ BG ). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH * ( S * ( G ), S * ( G )) of the singular chains of G is a Batalin–Vilkovisky algebra.

September 26, 2011

Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products

Ngaiming Mok, Sui Chung Ng

Page range: 47-73

Abstract

Let X be the quotient of an irreducible bounded symmetric domain Ω by a lattice. In order to characterize algebraic correspondences on X commuting with exterior Hecke correspondences, Clozel–Ullmo studied certain germs of measure-preserving maps from (Ω; 0) into its Cartesian products, proving that such maps are totally geodesic when dim( X ) = 1. Here we prove total geodesy when dim(Ω) ≧ 2 by methods of analytic continuation. For B n , n ≧ 2, total geodesy follows then from Alexander's theorem. When rank(Ω) ≧ 2, we deduce total geodesy from Alexander-type theorems, especially from a new Alexander-type theorem involving Reg(∂Ω) in place of the Shilov boundary.

October 5, 2011

Weak Neumann implies Stokes

Matthias Geissert, Horst Heck, Matthias Hieber, Okihiro Sawada

Page range: 75-100

Abstract

Consider a domain Ω ⊂ ℝ n with possibly non compact but uniform C 3 -boundary and assume that the Helmholtz projection P exists on L p (Ω) for some 1 < p < ∞. It is shown that the Stokes operator in L p (Ω) generates an analytic semigroup on admitting maximal L q - L p -regularity. Moreover, for there exists a unique local mild solution to the Navier–Stokes equations on domains of this form provided p > n .

October 11, 2011

Quasi-isometric classification of non-geometric 3-manifold groups

Jason A. Behrstock, Walter D. Neumann

Page range: 101-120

Abstract

We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have “too many” arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of 3-manifold groups in all but a few exceptional cases.

September 27, 2011

Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

Keiji Matsumoto, Tomohide Terasoma

Page range: 121-149

Abstract

In this paper, we give a Thomae type formula for K 3 surfaces X given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type I 22 and period integrals of X . Moreover, we express the period integrals by using the hypergeometric function F S of four variables. As applications of our main theorem, we define ℝ 4 -valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function F S .

September 26, 2011

Cosmetic crossing changes of fibered knots

Kalfagianni Efstratia

Page range: 151-164

Abstract

We prove the nugatory crossing conjecture for fibered knots. We also show that if a knot K is n -adjacent to a fibered knot K ′, for some n > 1, then either the genus of K is larger than that of K ′ or K is isotopic to K ′.

September 27, 2011

Leavitt path algebras of separated graphs

Pere Ara, Kenneth R. Goodearl

Page range: 165-224

Abstract

The construction of the Leavitt path algebra associated to a directed graph E is extended to incorporate a family C consisting of partitions of the sets of edges emanating from the vertices of E . The new algebras, L K ( E , C ), are analyzed in terms of their homology, ideal theory, and K -theory. These algebras are proved to be hereditary, and it is shown that any conical abelian monoid occurs as the monoid 𝒱( L K ( E , C )) of isomorphism classes of finitely generated projective modules over one of these algebras. The lattice of trace ideals of L K ( E , C ) is determined by graph-theoretic data, namely as a lattice of certain pairs consisting of a subset of E 0 and a subset of C . Necessary conditions for 𝒱( L K ( E , C )) to be a refinement monoid are developed, together with a construction that embeds ( E , C ) in a separated graph ( E + , C + ) such that 𝒱( L K ( E + , C + )) has refinement.

September 26, 2011

Brauer's height zero conjecture for the 2-blocks of maximal defect

Gabriel Navarro, Pham Huu Tiep

Page range: 225-247

Abstract

We prove Brauer's height zero conjecture on blocks of finite groups for every 2-block of maximal defect.

About this journal

The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of "Crelle's Journal". In the 190 years of its existence, "Crelle's Journal" has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI's Journal Citation Report.