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You searched for +publisher:"University of Iowa" +contributor:("Kawamuro, Keiko"). Showing records 1 – 3 of 3 total matches.

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University of Iowa

1. Ramirez Aviles, Camila Alexandra. P-bigon right-veeringness and overtwisted contact structures.

Degree: PhD, Mathematics, 2017, University of Iowa

A contact structure is a maximally non-integrable hyperplane field ξ on an odd-dimensional manifold M. In 3-dimensional contact geometry, there is a fundamental dichotomy, where a contact structure is either tight or overtwisted. Making use of Giroux's correspondence between contact structures and open books for 3-dimensional manifolds, Honda, Kazez, and Matíc proved that verifying whether a mapping class is right-veering or not gives a way of detecting tightness of the compatible contact structure. As a counter-part to right-veering mapping classes, right-veering closed braids have been studied by Baldwin and others. Ito and Kawamuro have shown how various results on open books can be translated to results on closed braids; introducing the notion of quasi right-veering closed braids to provide a sufficient condition which guarantees tightness. We use the related concept of P-bigon right-veeringness for closed braids to show that given a 3-dimensional contact manifold (M, ξ) supported by an open book (S, φ), if L \subset (M, ξ) is a non-P-bigon right-veering transverse link in pure braid position with respect to (S, φ), performing 0-surgery along L produces an overtwisted contact manifold (M', ξ'). Furthermore, if we suppose L \subset (M, ξ) is a pure and non-quasi right-veering braid with respect to (S, φ), performing p-surgery along L, for p  ≥  0, gives rise to an open book (S', φ') which supports an overtwisted contact manifold (M', ξ'). Advisors/Committee Members: Kawamuro, Keiko (supervisor).

Subjects/Keywords: contact geometry; contact structures; contact topology; overtwisted contact structures; p-bigon right-veeringness; Mathematics

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APA (6th Edition):

Ramirez Aviles, C. A. (2017). P-bigon right-veeringness and overtwisted contact structures. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/5609

Chicago Manual of Style (16th Edition):

Ramirez Aviles, Camila Alexandra. “P-bigon right-veeringness and overtwisted contact structures.” 2017. Doctoral Dissertation, University of Iowa. Accessed July 16, 2019. https://ir.uiowa.edu/etd/5609.

MLA Handbook (7th Edition):

Ramirez Aviles, Camila Alexandra. “P-bigon right-veeringness and overtwisted contact structures.” 2017. Web. 16 Jul 2019.

Vancouver:

Ramirez Aviles CA. P-bigon right-veeringness and overtwisted contact structures. [Internet] [Doctoral dissertation]. University of Iowa; 2017. [cited 2019 Jul 16]. Available from: https://ir.uiowa.edu/etd/5609.

Council of Science Editors:

Ramirez Aviles CA. P-bigon right-veeringness and overtwisted contact structures. [Doctoral Dissertation]. University of Iowa; 2017. Available from: https://ir.uiowa.edu/etd/5609


University of Iowa

2. Hamer, Jesse A. On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities.

Degree: PhD, Mathematics, 2018, University of Iowa

We investigate various forms of link positivity: braid positivity, strong quasipositivity, and quasi- positivity. On the one hand, this investigation is undertaken in the context of braid simplification: we give sufficient conditions under which a given braid word is conjugate to a braid word with strictly fewer negative bands. On the other hand, we use the famous Bennequin inequality to define a new link invariant: the defect of the Bennequin inequality, or 3-defect, and give criteria in terms of the 3-defect under which a given link is (strongly) quasipositive. Moreover, we use the 4-dimensional analogue of the Bennequin inequality, the slice Bennequin inequality in order to define the analogous defect of the slice Bennequin inequality, or 4-defect. We then investigate the relationship between the 4-defect and the most complicated class of 3- braids, Xu’s NP-form 3-braids, and establish several bounds. We also conjecture a formula for the signature of NP-form 3-braids which uses a new and easily computable NP-form 3-braid invariant, the offset. Finally, the appendices provide lists of all quasipositive and strongly quasipositive knots with at most 12 crossings (with two exceptions, 12n239 and 12n512), along with accompanying quasipositive or strongly quasipositive braid words. Many of these knots did not have previously established positivities or braid words reflecting these positivities—these facts were discovered using various criteria (conjectural or proven) expressed throughout this thesis. Advisors/Committee Members: Kawamuro, Keiko (supervisor).

Subjects/Keywords: Bennequin Inequality; Braid Theory; Contact Geometry; Strongly Quasipositive; Topology; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Hamer, J. A. (2018). On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/6587

Chicago Manual of Style (16th Edition):

Hamer, Jesse A. “On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities.” 2018. Doctoral Dissertation, University of Iowa. Accessed July 16, 2019. https://ir.uiowa.edu/etd/6587.

MLA Handbook (7th Edition):

Hamer, Jesse A. “On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities.” 2018. Web. 16 Jul 2019.

Vancouver:

Hamer JA. On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities. [Internet] [Doctoral dissertation]. University of Iowa; 2018. [cited 2019 Jul 16]. Available from: https://ir.uiowa.edu/etd/6587.

Council of Science Editors:

Hamer JA. On positivities of links: an investigation of braid simplification and defect of Bennequin inequalities. [Doctoral Dissertation]. University of Iowa; 2018. Available from: https://ir.uiowa.edu/etd/6587


University of Iowa

3. Ortiz, Marcos A. Convex decomposition techniques applied to handlebodies.

Degree: PhD, Mathematics, 2015, University of Iowa

Contact structures on 3-manifolds are 2-plane fields satisfying a set of conditions. The study of contact structures can be traced back for over two-hundred years, and has been of interest to mathematicians such as Hamilton, Jacobi, Cartan, and Darboux. In the late 1900's, the study of these structures gained momentum as the work of Eliashberg and Bennequin described subtleties in these structures that could be used to find new invariants. In particular, it was discovered that contact structures fell into two classes: tight and overtwisted. While overtwisted contact structures are relatively well understood, tight contact structures remain an area of active research. One area of active study, in particular, is the classification of tight contact structures on 3-manifolds. This began with Eliashberg, who showed that the standard contact structure in real three-dimensional space is unique, and it has been expanded on since. Some major advancements and new techniques were introduced by Kanda, Honda, Etnyre, Kazez, Matić, and others. Convex decomposition theory was one product of these explorations. This technique involves cutting a manifold along convex surfaces (i.e. surfaces arranged in a particular way in relation to the contact structure) and investigating a particular set on these cutting surfaces to say something about the original contact structure. In the cases where the cutting surfaces are fairly nice, in some sense, Honda established a correspondence between information on the cutting surfaces and the tight contact structures supported by the original manifold. In this thesis, convex surface theory is applied to the case of handlebodies with a restricted class of dividing sets. For some cases, classification is achieved, and for others, some interesting patterns arise and are investigated. Advisors/Committee Members: Kawamuro, Keiko (supervisor).

Subjects/Keywords: publicabstract; convex decomposition; cotact topology; topology; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Ortiz, M. A. (2015). Convex decomposition techniques applied to handlebodies. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/1713

Chicago Manual of Style (16th Edition):

Ortiz, Marcos A. “Convex decomposition techniques applied to handlebodies.” 2015. Doctoral Dissertation, University of Iowa. Accessed July 16, 2019. https://ir.uiowa.edu/etd/1713.

MLA Handbook (7th Edition):

Ortiz, Marcos A. “Convex decomposition techniques applied to handlebodies.” 2015. Web. 16 Jul 2019.

Vancouver:

Ortiz MA. Convex decomposition techniques applied to handlebodies. [Internet] [Doctoral dissertation]. University of Iowa; 2015. [cited 2019 Jul 16]. Available from: https://ir.uiowa.edu/etd/1713.

Council of Science Editors:

Ortiz MA. Convex decomposition techniques applied to handlebodies. [Doctoral Dissertation]. University of Iowa; 2015. Available from: https://ir.uiowa.edu/etd/1713

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