1,529 research outputs found
The equivariant K-theory of isotropy actions
We compute the equivariant K-theory with integer coefficients of an
equivariantly formal isotropy action, subject to natural hypotheses which cover
the three major classes of known examples. The proof proceeds by constructing a
map of spectral sequences from Hodgkin's K\"unneth spectral sequence in
equivariant K-theory to that in Borel cohomology. A new characterization of
equivariant formality appears as a consequence of this construction, and we are
now able to show that weak equivariant formality in the sense of
Harada--Landweber is equivalent with integer coefficients to surjectivity of
the forgetful map under a standard hypothesis.
The main structure theorem is formally similar to that for Borel equivariant
cohomology, which appears in the author's dissertation/dormant book project and
whose proof is finally made accessible in an appendix. The most generally
applicable corollary of the main theorem for rational coefficients depends on a
strengthening of the characterization of equivariant formality due to Shiga and
Takahashi, which appears as a second appendix.Comment: 22 pages. Comments extremely welcome
The Borel equivariant cohomology of real Grassmannians
Recent work of Chen He has determined through GKM methods the Borel
equivariant cohomology with rational coefficients of the isotropy action on a
real Grassmannian and an real oriented Grassmannian through GKM methods. In
this expository note, we propound a less involved approach, due essentially to
Vitali Kapovitch, to computing equivariant cohomology rings for
connected Lie groups, and apply it to recover the equivariant
cohomology of the Grassmannians. The bulk is setup and commentary; once one
believes in the model, the proof itself is under a page.Comment: 10-page expository note. Comments welcom
Equivariant formality of isotropic torus actions
Considering the potential equivariant formality of the left action of a
connected Lie group on the homogeneous space , we arrive through a
sequence of reductions at the case is compact and simply-connected and
is a torus.
We then classify all pairs such that is compact connected Lie and
the embedded circular subgroup acts equivariantly formally on . In the
process we provide what seems to be the first published proof of the structure
(known to Leray and Koszul) of the cohomology rings .Comment: Completely revised. Many proofs simplified, including reduction to
toral isotropy and classification of reflected circles. An error in the
reduction to the semisimple case is corrected. New: a reduction to the
compact case; partial reductions if the groups are disconnected or compact
but not Lie. Citations to literature improved. To be published in the Journal
of Homotopy and Related Structure
Special Education in Catholic Schools Viewed from a Liberatory Hermeneutic
This study explores anew the issue of providing special education in Catholic schools by viewing the ethical implications from a liberatory hermeneutic. By utilizing an interdisciplinary perspective, the research draws upon liberation theology, liberation psychology, liberation pedagogy, and liberation ethics to support the moral mandate for providing education for all God’s children, including those persons with disabilities. The study challenges Catholic educational leaders to reimagine their positions on how schools might promote a more inclusive, liberatory approach to serving the special needs of children with disabilities. Finally, this research provides a Catholic, liberatory, ethical framework for inclusive Catholic education to assist school leaders in the development of appropriate pedagogy and programming to address the issue of inclusion of students with disabilities
Effects of movements in equities prices on M2 demand
Large swings in stock prices are sometimes associated with a redirection of household savings flows. Such changes can lead to transitory increases in M2 as investors temporarily “park” funds in depository assets while they determine the funds’ ultimate destination. The authors find that, although stock price changes are statistically significant as an explanation for M2 growth, they do not account for much of M2’s recent strength.Stock - Prices ; Demand for money
Products on Tor
In 1974 work establishing the collapse of certain Eilenberg-Moore spectral
sequences, Munkholm constructs, in passing, a bilinear multiplication operation
on Tor of a triple of -algebras. In 2020, the present author,
pursuing a multiplicative collapse result extending Munkholm's, studied a
variant of this product, without actually showing it agrees with Munkholm's. In
2019, Franz had defined a weak product on the two-sided bar construction of a
triple of -algebras under similar hypotheses, with which this author
proved a related collapse result, but without investigating the properties of
the induced product on Tor.
The present work demonstrates that the two products on Tor agree and are
induced by the product of Franz.Comment: 19 pages, comments welcom
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Assessment of Ozone Initiated Chemistry in Portable Classrooms
A model was developed to predict concentrations of homogeneous and heterogeneous
ozone initiated reaction by-products in portable classrooms. The resulting estimates offer
reference values for highly occupied indoor environments. Indoor concentrations of
formaldehyde (HCHO), 4-oxopentanal (4-OPA), 6-methyl-5-hepten-2-one (6-MHO), and
secondary organic aerosols (SOA) were predicted based on various parameters of
specific portable classrooms in central Texas. The results were not significant to raise
concern for formaldehyde, but they did yield relatively high average and maximum
concentrations of 4-OPA, 6-MHO, and SOA. While the health implications of SOA are
more well known, less has been done to determine the toxicological effects of 4-OPA and
6-MHO. The results of this report indicate that more research should be conducted to
further understand the effects of these compounds on the indoor environment, as well as
human health.Civil, Architectural, and Environmental Engineerin
Fixed points and semifree bordism
We apply fixed-point techniques to compute the coefficient ring of semifree
geometric circle-equivariant complex cobordism with isolated fixed points,
recovering a 2004 result of Sinha through 19th-century methods. This should be
viewed as an initial proof-of-concept for a larger program employing the
Atiyah-Bott/Berline-Vergne localization theorem and Chern numbers in Borel
cohomology to compute equivariant complex cobordism.Comment: 5 pages; comments gratefully accepte
The K-theory of the conjugation action
In 1999, Brylinski and Zhang computed the complex equivariant K-theory of the
conjugation self-action of a compact, connected Lie group with torsion-free
fundamental group. In this note we show it is possible to do so in under a
page.Comment: Same as the published version up to formatting. 2pp. plus reference
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