5,211 research outputs found
Conjugation spaces and edges of compatible torus actions
Duistermaat introduced the concept of ``real locus'' of a Hamiltonian
manifold. In that and in others' subsequent works, it has been shown that many
of the techniques developed in the symplectic category can be used to study
real loci, so long as the coefficient ring is restricted to the integers modulo
2. It turns out that these results seem not necessarily to depend on the
ambient symplectic structure, but rather to be topological in nature. This
observation prompts the definition of ``conjugation space'' in a paper of the
two authors with V. Puppe. Our main theorem in this paper gives a simple
criterion for recognizing when a topological space is a conjugation space.Comment: 19 page
Braids: A Survey
This article is about Artin's braid group and its role in knot theory. We set
ourselves two goals: (i) to provide enough of the essential background so that
our review would be accessible to graduate students, and (ii) to focus on those
parts of the subject in which major progress was made, or interesting new
proofs of known results were discovered, during the past 20 years. A central
theme that we try to develop is to show ways in which structure first
discovered in the braid groups generalizes to structure in Garside groups,
Artin groups and surface mapping class groups. However, the literature is
extensive, and for reasons of space our coverage necessarily omits many very
interesting developments. Open problems are noted and so-labelled, as we
encounter them.Comment: Final version, revised to take account of the comments of readers. A
review article, to appear in the Handbook of Knot Theory, edited by W.
Menasco and M. Thistlethwaite. 91 pages, 24 figure
Binding stakeholders into moral communities: A review of studies on social responsibility of business
This paper revisits the issue of business social responsibility with a view to reiterate its relevance in the contemporary scenario characterised by an overarching presence of private businesses and blurring of the barriers between not-for-profit and for-profit enterprises. The paper reviews the evolution of major theoretical positions of business social responsibility to demonstrate how the basic understanding of the term traversed through time and alongside changes in forms of business organisation and interpretations of the morality of private property. It draws on stakeholding and social contract theories to underscore the moral and social responsibility of businesses to broaden their vision beyond profit and stakeholder value.social responsibility, stakeholder, social contract, moral communities
Computation of generalized equivariant cohomologies of Kac-Moody flag varieties
In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective
varieties X equipped with an algebraic action of a complex torus T, the
equivariant cohomology ring H_T(X) can be described by combinatorial data
obtained from its orbit decomposition. In this paper, we generalize their
theorem in three different ways. First, our group G need not be a torus.
Second, our space X is an equivariant stratified space, along with some
additional hypotheses on the attaching maps. Third, and most important, we
allow for generalized equivariant cohomology theories E_G^* instead of H_T^*.
For these spaces, we give a combinatorial description of E_G(X) as a subring of
\prod E_G(F_i), where the F_i are certain invariant subspaces of X. Our main
examples are the flag varieties G/P of Kac-Moody groups G, with the action of
the torus of G. In this context, the F_i are the T-fixed points and E_G^* is a
T-equivariant complex oriented cohomology theory, such as H_T^*, K_T^* or
MU_T^*. We detail several explicit examples.Comment: 19 pages, 6 figures, this is a new and completely modified version of
DG/040207
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