296 research outputs found
On a notion of maps between orbifolds, II. homotopy and CW-complex
This is the second of a series of papers which are devoted to a comprehensive
theory of maps between orbifolds. In this paper, we develop a basic machinery
for studying homotopy classes of such maps. It contains two parts: (1) the
construction of a set of algebraic invariants -- the homotopy groups, and (2)
an analog of CW-complex theory. As a corollary of this machinery, the classical
Whitehead theorem which asserts that a weak homotopy equivalence is a homotopy
equivalence is extended to the orbifold category.Comment: 51 pages, Communications in Contemporary Mathematics, to appea
On a notion of maps between orbifolds, I. function spaces
This is the first of a series of papers which are devoted to a comprehensive
theory of maps between orbifolds. In this paper, we define the maps in the more
general context of orbispaces, and establish several basic results concerning
the topological structure of the space of such maps. In particular, we show
that the space of such maps of C^r-class between smooth orbifolds has a natural
Banach orbifold structure if the domain of the map is compact, generalizing the
corresponding result in the manifold case. Motivations and applications of the
theory come from string theory and the theory of pseudoholomorphic curves in
symplectic orbifolds.Comment: Final version, 46 pages. Accepted for publication in Communications
in Contemporary Mathematics. A preliminary version of this work is under a
different title "A homotopy theory of orbispaces", arXiv: math. AT/010202
Cohomology of Coxeter groups with group ring coefficients: II
For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules
and then compute the associated graded terms. More generally, if U is a CW
complex on which W acts as a reflection group we compute the associated graded
terms for H_*(U) and, in the case where the action is proper and cocompact, for
H^*_c(U).Comment: This is the version published by Algebraic & Geometric Topology on 15
September 200
A classification of smooth embeddings of 3-manifolds in 6-space
We work in the smooth category. If there are knotted embeddings S^n\to R^m,
which often happens for 2m<3n+4, then no concrete complete description of
embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint
unions of spheres. Let N be a closed connected orientable 3-manifold. Our main
result is the following description of the set Emb^6(N) of embeddings N\to R^6
up to isotopy.
The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in
H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where
d(u) is the divisibility of the projection of u to the free part of H_1(N;Z).
The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on
Emb^6(N) by embedded connected sum. It was proved that the orbit space of this
action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's
smoothing theory). The new part of our classification result is determination
of the orbits of the action. E. g. for N=RP^3 the action is free, while for
N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that
for each knot l:S^3\to R^6 the embedding f#l is isotopic to f.
Our proof uses new approaches involving the Kreck modified surgery theory or
the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in
Math. Zei
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Carrots and Rainbows: Motivation and Social Practice in Open Source Software Development
Open source software (OSS) is a social and economic phenomenon that raises fundamental questions about the motivations of contributors to information systems development. Some developers are unpaid volunteers who seek to solve their own technical problems, while others create OSS as part of their employment contract. For the past 10 years, a substantial amount of academic work has theorized about and empirically examined developer motivations. We review this work and suggest considering motivation in terms of the values of the social practice in which developers participate. Based on the social philosophy of Alasdair MacIntyre, we construct a theoretical framework that expands our assumptions about individual motivation to include the idea of a long-term, value-informed quest beyond short-term rewards. This motivation-practice framework depicts how the social practice and its supporting institutions mediate between individual motivation and outcome. The framework contains three theoretical conjectures that seek to explain how collectively elaborated standards of excellence prompt developers to produce high-quality software, change institutions, and sustain OSS development. From the framework, we derive six concrete propositions and suggest a new research agenda on motivation in OSS
Cohomological tautness for Riemannian foliations
In this paper we present some new results on the tautness of Riemannian
foliations in their historical context. The first part of the paper gives a
short history of the problem. For a closed manifold, the tautness of a
Riemannian foliation can be characterized cohomologically. We extend this
cohomological characterization to a class of foliations which includes the
foliated strata of any singular Riemannian foliation of a closed manifold
Gauge Formalism for General Relativity and Fermionic Matter
A new formalism for spinors on curved spaces is developed in the framework of
variational calculus on fibre bundles. The theory has the same structure of a
gauge theory and describes the interaction between the gravitational field and
spinors. An appropriate gauge structure is also given to General Relativity,
replacing the metric field with spin frames. Finally, conserved quantities and
superpotentials are calculated under a general covariant form.Comment: 18 pages, Plain TEX, revision, explicit expression for superpotential
has been adde
Ossifying Fibroma of Non-odontogenic Origin: A Fibro-osseous Lesion in the Craniofacial Skeleton to be (Re-)considered
In the cranio-facial skeleton, a heterogeneous group of well characterized fibro-osseous lesions can be distinguished. Whereas fibrous dysplasia can affect any skeletal bone, ossifying fibroma and cemento-osseous dysplasia exclusively develop in the cranio-facial region, with most subtypes restricted to the tooth bearing areas of the jaws. Herein we present a series of 20 fibro-osseous lesions that developed mostly in the frontal bone and in the mandible, presenting as expansile intramedullary tumors with a unique histologic appearance and an indolent clinical course. We provide evidence that these tumors are distinct from the categories included in the WHO classification and are therefore currently unclassifiable. The definition of cemento-ossifying fibroma as an odontogenic neoplasm developing only in close proximity to teeth should be re-considered and incorporate also extragnathic lesions as shown here
Cohomology of bundles on homological Hopf manifold
We discuss the properties of complex manifolds having rational homology of
including those constructed by Hopf, Kodaira and
Brieskorn-van de Ven. We extend certain previously known vanishing properties
of cohomology of bundles on such manifolds.As an application we consider
degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex
variables and Complex Geometry. Xiamen. Chin
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
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