400 research outputs found

    Quasi-isometric groups with no common model geometry

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    A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly and cocompactly by isometries on the same proper geodesic metric space, then the groups are commensurable. Consequently, there are infinitely many fundamental groups of simple surface amalgams that are quasi-isometric, but which do not act properly and cocompactly on the same proper geodesic metric space.Comment: v2: 19 pages, 6 figures; minor changes. To appear in Journal of the London Mathematical Societ

    Hyperbolic groups that are not commensurably coHopfian

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    Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every simple surface amalgam is not commensurably coHopfian.Comment: v3: 14 pages, 4 figures; minor changes. To appear in International Mathematics Research Notice

    The visual boundary of hyperbolic free-by-cyclic groups

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    Let ϕ\phi be an atoroidal outer automorphism of the free group FnF_n. We study the Gromov boundary of the hyperbolic group Gϕ=FnϕZG_{\phi} = F_n \rtimes_{\phi} \mathbb{Z}. We explicitly describe a family of embeddings of the complete bipartite graph K3,3K_{3,3} into Gϕ\partial G_\phi. To do so, we define the directional Whitehead graph and prove that an indecomposable FnF_n-tree is Levitt type if and only if one of its directional Whitehead graphs contains more than one edge. As an application, we obtain a direct proof of Kapovich-Kleiner's theorem that Gϕ\partial G_\phi is homeomorphic to the Menger curve if the automorphism is atoroidal and fully irreducible.Comment: 25 pages, 3 figure

    Real-Life Solutions to Real-Life Problems: Collaborating with a Non-Profit Foundation to Engage Honors Students in Applied Research

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    Colleges and universities have long emphasized undergraduate research experiences as valuable activities for students. The National Science Foundation (NSF) echoed this focus in 2003, recommending that all students get involved in undergraduate research as early as possible in their college careers (NSF). Collegiate honors programs in particular have embraced the role of student research as an integral experience for high-ability students, leading the way in developing the thesis-based model of undergraduate research that is increasingly common in institutions of higher learning

    Using John Grisham\u27s The Innocent Man to Create a Significant Learning Experience for Undergraduate Students in a Psychology and the Law Course

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    Imagine a man, suffering from alcoholism and schizophrenia, drifting through his small town, known mostly for getting thrown out of bars. When a graphic murder occurs, this man’s name gets linked to the victim, and police focus on him as a suspect. Although there is no evidence against him, a combination of poor police work and a town’s desire for closure lead to this innocent man being convicted of the crime and sentenced to death. Down to his last appeal, after spending 12 years on death row, a fair and honest judge is finally convinced to take a closer look at this man’s case, and he is eventually freed. These are the true events that happened to Ron Williamson, sent to death row for a murder he didn’t commit, and his story is told in John Grisham’s only non-fiction book, The Innocent Man: Murder and Injustice in a Small Town. I chose to use this book as assigned reading in my Psychology and the Law course to introduce students to topics related to our legal system through the lens of a true case of a man wrongly convicted. The course is a lower-level psychology course, designed for students interested in learning more about forensic psychology and other topics related to psychology and the legal system. The students in the course were mostly sophomore, junior and senior psychology majors. Several law enforcement majors and corrections majors were also enrolled. In the course, we covered areas including forensic psychology and determining competence, interrogations and false confessions, lie detection and polygraphs, eyewitness memory, racism in the courtroom, jury decision-making, and the death penalty. The book The Innocent Man was a natural fit with the course; it raises issues of determining competency and how our legal system deals with people with mental health problems. The book also explores false confessions, flawed eyewitness testimony, jail snitches, police and prosecutors under pressure, courtroom trials and jury decisions, death penalty sentencing, and the appeals process. I wanted students to be able to learn more about the process of investigation, trials, and appeals, while also seeing the effect that mistakes can have on the human beings involved. Although students also read assigned textbook chapters, I hoped that The Innocent Man would reinforce these concepts while engaging the students with this real-life story

    Real Life Solutions to Real Life Problems: Collaborating with a Non-Profit Foundation to Engage Honors Students in Applied Research

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    Colleges and universities have long emphasized undergraduate research experiences as valuable activities for students. The National Science Foundation (NSF) echoed this focus in 2003, recommending that all students get involved in undergraduate research as early as possible in their college careers (NSF). Collegiate honors programs in particular have embraced the role of student research as an integral experience for high-ability students, leading the way in developing the thesis-based model of undergraduate research that is increasingly common in institutions of higher learning. However, one difficulty in getting honors students involved in research, particularly early in their years at college, is that they misunderstand what research entails or see it only as the province of laboratory-based science majors. Even in social science programs such as psychology or sociology or in applied programs such as nursing or communication studies, where empirical research is central to the discipline, students may not understand the value of research in these contexts or may think that they do not have the skills or ideas to participate in the research process. When asked to define research, many students think only of laboratories, test tubes, and technical equipment, or they think of the ubiquitous research papers that they have already encountered in their classes and that they often see as summarizing the ideas of other people rather than contributing new knowledge. Since the spring of 2012, the Minnesota State University, Mankato Honors Program has partnered with the Southern Minnesota Initiative Foundation (SMIF) to implement two separate approaches to developing honors students\u27 research skills and broadening their understanding of the research process. We incorporated applied research opportunities for honors students in two different settings: a course on research methods and an independent study research experience. Each approach was successful at building students\u27 confidence in their research skills, giving them experience with applied research practices, and broadening their understanding of what constitutes research. Each approach had various pros and cons that might be useful to other programs with plans to develop similar opportunities, and I include recommendations for how to form connections with community groups. The reflections completed by students who participated in these opportunities provide important perspectives that supplement my own as the instructor and faculty mentor for these experiences. Finally, in Appendix A I provide a letter from the president of the Southern Minnesota Initiative Foundation presenting his perception of their partnership with our Honors program

    An Investigation of Perspectives on Mental Illness Across Race and Ethnicity

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    Previous research done on mental illness stigma and race and ethnicity has failed to properly recognize the complexity of identity and cultural influences and how these factors impact people’s perceptions of mental illness. These studies tend to insinuate that any differences of beliefs found between groups are due to race or ethnicity, when in fact this is an imprudent conclusion. In this thesis, a critical analysis of the literature on mental illness stigma and race and ethnicity determines that categorizing people into large homogenous groups based on race or ethnicity results in an inaccurate picture of what people believe about mental illness. Qualitative interviews conducted with young adults determined three common factors that influence beliefs about mental illness: religion, age or generation, and socioeconomic status. A quantitative survey was then used to get the perspective of a larger sample. The results of this study demonstrate differences and similarities of beliefs both within and across racial and ethnic groups for all three factors. There were few consistencies in specific beliefs within racial or ethnic groups, which supports the argument that differences in beliefs between groups cannot be explained solely by racial or ethnic differences. The results of this study show the importance of using a mixed methods approach that recognizes intersectionality by illustrating the complexity of identity, especially when it comes to the relationship between identity and beliefs about mental illness. --Provided by author
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