917 research outputs found
Tori and Heegaard splittings
Haken showed that the Heegaard splittings of reducible 3-manifolds are
reducible, that is, a reducing 2-sphere can be found which intersects the
Heegaard surface in a single simple closed curve. When the genus of the
"interesting" surface increases from zero, more complicated phenomena occur.
Kobayashi showed that if a 3-manifold contains an essential torus ,
then it contains one which can be isotoped to intersect a strongly irreducible
Heegaard splitting surface in a collection of simple closed curves which
are essential in and in . In general there is no global bound on the
number of curves in this collection. We give conditions under which a global
bound can be obtained
Dehn surgery on complicated fibered knots in the 3-sphere
Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K
is sufficiently complicated, then Dehn surgery on K cannot yield a lens space.
Work of Yi Ni shows that if K has a lens space surgery then it is fibered.
Combining this with our result we see that if K has a lens space surgery then
it is fibered and the monodromy is relatively simple
On tunnel number one knots that are not (1,n)
We show that the bridge number of a bridge knot in with respect to
an unknotted genus surface is bounded below by a function of the distance
of the Heegaard splitting induced by the bridges. It follows that for any
natural number , there is a tunnel number one knot in that is not
.Comment: 7 page
Knots and k-width
We investigate several integer invariants of curves in 3-space. We
demonstrate relationships of these invariants to crossing number and to total
curvature
Climate Change and Voluntary Private Land Conservation: A Case Study of Working Lands for Wildlife
This case study examines the role, impact, and future of voluntary private land conservation (VPLC) programs, with a particular focus on the U.S. Department of Agriculture’s Working Lands for Wildlife (WLFW) initiative. Climate change and population growth pose a significant threat to public land conservation, making alternative methods like WLFW increasingly important. WLFW is a relatively successful and well-received program, but it is still young and comparatively smaller than other VPLC programs operated by the government. Publications by the U.S. Department of Agriculture, WLFW partner organizations, and relevant scholarly articles were utilized in order to assess WLFW’s success independently and in comparison with other federal VPLC programs. With additional funding and new strategies for enrolling participants, WLFW may be able to increase its capacity and become a flagship VPLC program. If this initial expansion is successful enough, WLFW leadership may consider further expanding the program to also enroll non-agricultural privately owned land, primarily recreational land used for hunting, fishing, or wildlife watching
Community Art Installation As An Approach To Art Therapy: A Community Engagement
In this thesis capstone paper, I advocate for a community art installation as an ethical and engaging way to approach art therapy. I argue that this approach may blur the lines between art therapy, art education and arts activism, but it is a powerful and anti-oppressive way to facilitate healing in marginalized communities. I found this approach furthered my understanding of what it means to be a competent and ethical art therapist. I also found it empowered art therapy group members and made them active facilitators of change in their lives and their communities. Observing the success of this project suggests a paradigm shift in approaches to art therapy
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