3,804 research outputs found
Fractional Dehn twists in knot theory and contact topology
Fractional Dehn twists give a measure of the difference between the relative
isotopy class of a homeomorphism of a bordered surface and the Thurston
representative of its free isotopy class. We show how to estimate and compute
these invariants. We discuss the the relationship of our work to stabilization
problems in classical knot theory, general open book decompositions, and
contact topology. We include an elementary characterization of overtwistedness
for contact structures described by open book decompositions.Comment: We have removed an incorrect assumption about properties of
meridional disks of Heegaard decompositions of S^3 and have added a
conjecture about stabilizations of knots in S^
Public geographies II: being organic
This second report on âpublic geographies' considers the diverse, emergent and shifting spaces of engaging with and in public/s. Taking as its focus the more âorganicâ rather than âtraditionalâ approach to doing public geography, as discussed in the first report, it explores the multiple and unorthodox ways in which engagements across academic-public spheres play out, and what such engagements may mean for geography/ers. The report first explores the role of the internet in âenabling conversations', generating a range of opportunities for public geography through websites, wikis, blogs, file-sharing sites, discussion forums and more, thinking critically about how technologies may enable/disable certain kinds of publically engaged activities. It then considers issues of process and praxis: how collaborations with groups/communities/organizations beyond academia are often unplanned, serendipitous encounters that evolve organically into research/learning/teaching endeavours; but also that personal politics/positionality bring an agency to bear upon whether we, as academics, follow the leads we may stumble upon. The report concludes with a provocative question â given that many non-academics appear to be doing some amazing and inspiring projects and activities, thoughtful, critical and (arguably) examples of organic public geographies, what then is academiaâs role
Weak and strong fillability of higher dimensional contact manifolds
For contact manifolds in dimension three, the notions of weak and strong
symplectic fillability and tightness are all known to be inequivalent. We
extend these facts to higher dimensions: in particular, we define a natural
generalization of weak fillings and prove that it is indeed weaker (at least in
dimension five),while also being obstructed by all known manifestations of
"overtwistedness". We also find the first examples of contact manifolds in all
dimensions that are not symplectically fillable but also cannot be called
overtwisted in any reasonable sense. These depend on a higher-dimensional
analogue of Giroux torsion, which we define via the existence in all dimensions
of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor
edits. v3: exposition improved using referee's comments. Published by Invent.
Mat
Sex and the Cinema: What American Pie Teaches the Young
This paper focuses upon the wildly successful blockbuster American Pie teenpics, especially American Pie 3 â the Wedding. I argue that these films, which are sited so securely within the visual and pedagogical machinery of Hollywood culture, are specifically designed to appeal to teenage male audiences, and to provide lessons in sex and romance. Movies like this are especially important as they are experienced by far more teenagers than, for example, instructional films or other classroom materials; indeed, as Henry Giroux has observed, "teens and youth learn how to define themselves outside of the traditional sites of instruction, such as the home and the school⊠Learning in the postmodern age is located elsewhere â in popular spheres that shape their identities, through forms of knowledge and desires that appear absent from what is taught in schools" (Giroux, 1997, p.49). In this paper I discuss whether the American Pie series is actually a "new age" effort which, via insubordinate performances of gender, contests the hegemonic field of signification which regulates the production of sex, gender and desire, or whether it is more accurately described as a retrogressive hetero-conservative opus with a veneer of sexual radicalism. In short, I intend to probe whether this filmic vector for sex education is all about the shaping of responsible, caring, vulnerable men, or is it guiding them to become just like their heterosexual, middle-class fathers? And whether, despite its riotous and raunchy advertising, American Pie really dishes up something spicy or something terribly wholesome instead
Tight contact structures and taut foliations
We show the equivalence of several notions in the theory of taut foliations
and the theory of tight contact structures. We prove equivalence, in certain
cases, of existence of tight contact structures and taut foliations.Comment: Published in Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper7.abs.htm
Towards a framework for critical citizenship education
Increasingly countries around the world are promoting forms of "critical" citizenship in the planned curricula of schools. However, the intended meaning behind this term varies markedly and can range from a set of creative and technical skills under the label "critical thinking" to a desire to encourage engagement, action and political emancipation, often labelled "critical pedagogy". This paper distinguishes these manifestations of the "critical" and, based on an analysis of the prevailing models of critical pedagogy and citizenship education, develops a conceptual framework for analysing and comparing the nature of critical citizenship
Brieskorn manifolds as contact branched covers of spheres
We show that Brieskorn manifolds with their standard contact structures are
contact branched coverings of spheres. This covering maps a contact open book
decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.Comment: 8 pages, 1 figur
Reinventing College Physics for Biologists: Explicating an epistemological curriculum
The University of Maryland Physics Education Research Group (UMd-PERG)
carried out a five-year research project to rethink, observe, and reform
introductory algebra-based (college) physics. This class is one of the Maryland
Physics Department's large service courses, serving primarily life-science
majors. After consultation with biologists, we re-focused the class on helping
the students learn to think scientifically -- to build coherence, think in
terms of mechanism, and to follow the implications of assumptions. We designed
the course to tap into students' productive conceptual and epistemological
resources, based on a theoretical framework from research on learning. The
reformed class retains its traditional structure in terms of time and
instructional personnel, but we modified existing best-practices curricular
materials, including Peer Instruction, Interactive Lecture Demonstrations, and
Tutorials. We provided class-controlled spaces for student collaboration, which
allowed us to observe and record students learning directly. We also scanned
all written homework and examinations, and we administered pre-post conceptual
and epistemological surveys. The reformed class enhanced the strong gains on
pre-post conceptual tests produced by the best-practices materials while
obtaining unprecedented pre-post gains on epistemological surveys instead of
the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material
Tight Beltrami fields with symmetry
Let be a compact orientable Seifered fibered 3-manifold without a
boundary, and an -invariant contact form on . In a suitable
adapted Riemannian metric to , we provide a bound for the volume
and the curvature, which implies the universal tightness of the
contact structure .Comment: 26 page
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