Taut foliations, braid positivity, and unknot detection

We study positive braid knots (the knots in the three-sphere realized as positive braid closures) through the lens of the L-space conjecture. This conjecture predicts that if $K$ is a non-trivial positive braid knot, then for all $r < 2g(K)-1$, the 3-manifold obtained via $r$-framed Dehn surgery along $K$ admits a taut foliation. Our main result provides some positive evidence towards this conjecture: we construct taut foliations in such manifolds whenever $r<g(K)+1$. As an application, we produce a novel braid positivity obstruction for cable knots by proving that the $(n,\pm 1)$-cable of a knot $K$ is braid positive if and only if $K$ is the unknot. We also present some curious examples demonstrating the limitations of our construction; these examples can also be viewed as providing some negative evidence towards the L-space conjecture. Finally, we apply our main result to produce taut foliations in some splicings of knot exteriors.Comment: 91 pages, 49 figures, 5 tables, 1 flowchart, 1 appendi

nn-bridge braids and the braid index

In this work, we find a closed form formula for the braid index of an $n$-bridge braid, a class of positive braid knots which simultaneously generalizes torus knots, 1-bridge braids, and twisted torus knots. Our proof is elementary, effective, and self-contained, and partially recovers work of Birman--Kofman. Along the way, we show that the disparate definitions of twisted torus knots in the literature agree.Comment: Accepted to "Journal of Knot Theory and its Ramifications

Brunnian exotic surface links in the 4-ball

This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two different constructions of exotic pairs of surface links that are Brunnian, meaning that all proper sublinks of the surface are trivial. We then modify these core constructions to vary the number of components in the exotic links, the genera of the components, and the number of components that must be removed before the surfaces become unlinked. Our arguments extend two tools from 3-dimensional knot theory into the 4-dimensional setting: satellite operations, especially Bing doubling, and covering links in branched covers.Comment: 37 pages, 36 figures, 2 appendices, 1 footnote, 1 stanz

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Taut foliations, positive braids, and the L-space conjecture:

Thesis advisor: Joshua E. GreeneWe construct taut foliations in every closed 3-manifold obtained by r-framed Dehn surgery along a positive 3-braid knot K in S^3, where r < 2g(K)-1 and g(K) denotes the Seifert genus of K. This confirms a prediction of the L--space conjecture. For instance, we produce taut foliations in every non-L-space obtained by surgery along the pretzel knot P(-2,3,7), and indeed along every pretzel knot P(-2,3,q), for q a positive odd integer. This is the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. We adapt our techniques to construct taut foliations in every closed 3-manifold obtained along r-framed Dehn surgery along a positive 1-bridge braid, and indeed, along any positive braid knot, in S^3, where r < g(K)-1. These are the only examples of theorems producing taut foliations in surgeries along hyperbolic knots where the interval of surgery slopes is in terms of g(K).Thesis (PhD) — Boston College, 2020.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics

Taut Foliations, Positive 3-Braids, and the L-Space Conjecture

The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll build taut foliations for manifolds obtained by surgery on positive 3-braid closures. Our theorem provides the first construction of taut foliations for every non-L-space obtained by surgery along an infinite family of hyperbolic L-space knots. As an example, we'll construct taut foliations in every non-L-space obtained by surgery along the P(-2,3,7) pretzel knot.Non UBCUnreviewedAuthor affiliation: Boston CollegeGraduat

ROS mediated MAPK signaling in abiotic and biotic stress- striking similarities and differences

Plants encounter a number of environmental stresses throughout their life cycles, most of which activate mitogen activated protein kinase (MAPK) pathway. The MAPKs show crosstalks at several points but the activation and the final response is known to be specific for particular stimuli that in-turn activates specific set of downstream targets. Interestingly, reactive oxygen species (ROS) is an important and common messenger produced in various environmental stresses and is known to activate many of the MAPKs. ROS activates a similar MAPK in different environmental stimuli, showing different downstream targets with different and specific responses. In animals and yeast, the mechanism behind the specific activation of MAPK by different concentration and species of ROS is elaborated, but in plants this aspect is still unclear. This review mainly focuses on the aspect of specificity of ROS mediated MAPK activation. Attempts have been made to review the involvement of ROS in abiotic stress mediated MAPK signaling and how it differentiates with that of biotic stress

Abstracts of Scientifica 2022

This book contains the abstracts of the papers presented at Scientifica 2022, Organized by the Sancheti Institute College of Physiotherapy, Pune, Maharashtra, India, held on 12–13 March 2022. This conference helps bring researchers together across the globe on one platform to help benefit the young researchers. There were six invited talks from different fields of Physiotherapy and seven panel discussions including over thirty speakers across the globe which made the conference interesting due to the diversity of topics covered during the conference. Conference Title:  Scientifica 2022Conference Date: 12–13 March 2022Conference Location: Sancheti Institute College of PhysiotherapyConference Organizer: Sancheti Institute College of Physiotherapy, Pune, Maharashtra, Indi