On the Heegaard Floer homology of Dehn surgery and unknotting number

n this thesis we generalise three theorems from the literature on Heegaard Floer homology and Dehn surgery: one by Ozsv ́ath and Szab ́o on deficiency symmetries in half-integral L -space surgeries, and two by Greene which use Donaldson’s diagonali- sation theorem as an obstruction to integral and half-integral L -space surgeries. Our generalisation is two-fold: first, we eliminate the L -space conditions, opening these techniques up for use with much more general 3-manifolds, and second, we unify the integral and half-integral surgery results into a broader theorem applicable to non- zero rational surgeries in S 3 which bound sharp, simply connected, negative-definite smooth 4-manifolds. Such 3-manifolds are quite common and include, for example, a huge number of Seifert fibred spaces. Over the course of the first three chapters, we begin by introducing background material on knots in 3-manifolds, the intersection form of a simply connected 4- manifold, Spin- and Spin c -structures on 3- and 4-manifolds, and Heegaard Floer ho- mology (including knot Floer homology). While none of the results in these chapters are original, all of them are necessary to make sense of what follows. In Chapter 4, we introduce and prove our main theorems, using arguments that are predominantly algebraic or combinatorial in nature. We then apply these new theorems to the study of unknotting number in Chapter 5, making considerable headway into the extremely difficult problem of classifying the 3-strand pretzel knots with unknotting number one. Finally, in Chapter 6, we present further applications of the main theorems, ranging from a plan of attack on the famous Seifert fibred space realisation problem to more biologically motivated problems concerning rational tangle replacement. An appendix on the implications of our theorems for DNA topology is provided at the end.Open Acces

Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory

In flat space, the extreme Reissner-Nordstr\o m (RN) black hole is distinguished by its coldness (vanishing Hawking temperature) and its supersymmetry. We examine RN solutions to Einstein-Maxwell theory with a cosmological constant $\Lambda$, classifying the cold black holes and, for positive $\Lambda$, the ``lukewarm" black holes at the same temperature as the de Sitter thermal background. For negative $\Lambda$, we classify the supersymmetric solutions within the context of $N=2$ gauged supergravity. One finds supersymmetric analogues of flat-space extreme RN black holes, which for nonzero $\Lambda$ differ from the cold black holes. In addition, there is an exotic class of supersymmetric solutions which cannot be continued to flat space, since the magnetic charge becomes infinite in that limit.Comment: (18 pp., plain tex

Generalized Killing equations for spinning spaces and the role of Killing-Yano tensors

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables.Comment: LaTeX, 6 pages, Talk given at the International Symposium on the Theory of Elementary Particles, Buckow 199

The Rotating Dyonic Black Holes Of Kaluza-Klein Theory

The most general electrically and magnetically charged rotating black hole solutions of 5 dimensional \KK\ theory are given in an explicit form. Various classical quantities associated with the black holes are derived. In particular, one finds the very surprising result that the gyromagnetic and gyroelectric ratios can become {\tenit arbitrarily large}. The thermodynamic quantities of the black holes are calculated and a Smarr-type formula is obtained leading to a generalized first law of black hole thermodynamics. The properties of the extreme solutions are investigated and it is shown how they naturally separate into two classes. The extreme solutions in one class are found to have two unusual properties: (i). Their event horizons have zero angular velocity and yet they have non-zero ADM angular momentum. (ii). In certain circumstances it is possible to add angular momentum to these extreme solutions without changing the mass or charges and yet still maintain an extreme solution. Regarding the extreme black holes as elementary particles, their stability is discussed and it is found that they are stable provided they have sufficient angular momentum.Comment: 28 pages, LaTeX with 3 PostScript figure

The status of |Vub|

I survey the theoretical and experimental information available for determination of |Vub| with inclusive and exclusive techniques. Using recent experimental and theoretical advances, I outline a procedure in which the inclusive information can be combined to obtain an inclusive |Vub| that includes experimentally--derived uncertainty estimates for outstanding theoretical corrections.Comment: 9 pages, 5 figures, uses aipproc.cls, submitted to Proceedings of Beauty 200

Sessions v. Dimaya: Vagueness Doctrine & Deportation Statutes

Sessions v. Dimaya seeks to determine whether the residual clause of a criminal provision, incorporated by reference into a civil immigration law, is void for vagueness. Although there is an instance of the Supreme Court applying the criminal vagueness standard to an immigration statute resulting in deportation, the United States argues that immigration law is not subject to that vagueness standard because it is civil and not criminal. This commentary argues that Sessions v. Dimaya presents the Supreme Court with an opportunity to conform with its precedents, further the principles underlying vagueness doctrine, and appear to apply judicial rules consistently. To do so, the Court should apply the modern criminal vagueness analysis here, extending that analysis to immigration statutes resulting in deportation, and strike the indeterminate residual clause

Dilaton Black Holes Near the Horizon

Generic $U(1)^2$ 4-d black holes with unbroken $N=1$ supersymmetry are shown to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black holes, which have unbroken $N=2$ supersymmetry, behave near the horizon as a 2-d linear dilaton vacuum $\otimes \, S^2$. This geometry is invariant under 8 supersymmetries, i.e. half of the original $N=4$ supersymmetries are unbroken. The supersymmetric positivity bound, which requires the mass of the 4-d dilaton black holes to be greater than or equal to the central charge, corresponds to positivity of mass for a class of stringy 2-d black holes.Comment: 10 pages, SU-ITP-92-2

The evaluation of a breast cancer screening decision aid in the community setting.

Breast cancer screening (BCS) has been recommended to women by healthcare providers as well as professional organizations and non-profit awareness organizations for over four decades. Recently, attention is being paid to quantification of the actual benefits and harms of BCS with mammography. The harms include overdiagnosis, overtreatment and mandate of mammography screening that may not be in alignment with the individual values and preferences of women ages 40-69. This evidence translation project developed a resource for practice that was evaluated by community participants for alignment with personal value and preference-based educational needs about BCS. This project piloted a clinical practice decision aid (DA), called My Personal Decision (MPD), directly to a community-based convenience sample of women ages 40-69. Through a small sample of women, a change in knowledge about the harms and benefits of BCS was demonstrated. Evaluation feedback from the participants before and after use of the tool confirmed that MPD was helpful and enhanced preparedness for BCS decision-making. Provision of evidence-based information directly to women in the community setting was well received and perceived as valuable in the screening decision-making process in this context. Understanding of evidence-based information is a fundamental element in the empowerment of the decision maker with the goal of informed decision-making