121 research outputs found
Transesophageal drainage of an infected bronchogenous cyst via endoscopic ultrasound-guided implantation of a 7-Fr nasocystic drainage catheter
No full textKnot Floer homology, link Floer homology and link detection
No full textWe give new link detection results for knot and link Floer homology inspired
by recent work on Khovanov homology. We show that knot Floer homology detects
, , , , and the link with the
orientation of one component reversed. We show link Floer homology detects
and , for all . Additionally we identify infinitely many
pairs of links such that both links in the pair are each detected by link Floer
homology but have the same Khovanov homology and knot Floer homology. Finally,
we use some of our knot Floer detection results to give topological
applications of annular Khovanov homology
Floer homology, clasp-braids and detection results
No full textMartin showed that link Floer homology detects braid axes. In this paper we
extend this result to give a topological characterisation of links which are
almost braided from the point of view of link Floer homology. The result is
inspired by work of Baldwin-Sivek and Li-Ye on nearly fibered knots.
Applications include that Khovanov homology detects the Whitehead link and
, as well as infinite families of detection results for link Floer
homology and annular Khovanov homology.Comment: 67 pages, 15 figure
Aspects of the Atiyah-Floer conjecture
No full textM.Phil.In this thesis, we will give a survey about the Atiyah-Floer Conjecture. The Atiyah-Floer conjecture asserts that two versions of Floer homology groups arising from a Heegaard splitting of a closed three manifold are isomorphic.In Chapter 0, we will introduce the Atiyah-Floer conjecture. In Chapter 1 and 2, we will review the construction of the two versions of Floer homology groups. Namely, the Lagrangian Floer homology and the instanton Floer homology respectively. In Chapter 3, we will discuss further constructions inspired by the conjecture.在這份論文，我們會給出有關Atiyah-Floer 猜想的綜述。Atiyah-Floer 猜想提出：來自一個閉三維流形的Heegaard 分解的兩種Floer 同調群是同構的。在第零章，我們會介紹Atiyah-Floer 猜想。在第一章及第二章，我們會重溫兩種版本的Floer 同調群的構造。亦即，Lagrangian Floer 同調及 Instanton Floer 同調。在第三章，我們會討論啟發自這個猜想的更進一步的建構。Li, Lok Tung.Thesis M.Phil. Chinese University of Hong Kong 2017.Includes bibliographical references (leaves 71-74).Abstracts also in Chinese.Title from PDF title page (viewed on 11, February, 2020)
Sore throat and subcutaneous emphysema in a 71-year-old patient
No full textA 71-year-old woman was admitted to our emergency department due to sore throat and swelling of the neck and face. She had a history of chronic obstructive pulmonary disease grade 4 based on the Global Initiative for Chronic Obstructive Lung Disease (GOLD). Clinical examination revealed subcutaneous emphysema of the neck and face. CT scan of the thorax and abdomen showed air in the retroperitoneum, ascending through the mediastinum into the neck and face. Laparotomy confirmed the diagnosis of a retroperitoneal colon perforation due to colon diverticulitis. The colon was partially removed followed by a surgical debridement and Hartmann's procedure. The postoperative course was without complications, the clinical symptoms resolved rapidly
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Bordered Sutured Floer Homology
No full textWe investigate the relationship between two versions of Heegaard Floer homology for 3-manifolds with boundary--the sutured Floer homology of Juhasz, and the bordered Heegaard Floer homology of Lipshitz, Ozsvath, and Thurston.
We define a new invariant called Bordered sutured Floer homology which encompasses these two invariants as special cases. Using the properties of this new invariant we prove a correspondence between the original bordered and sutured homologies.
In one direction we prove that for a 3-manifold with connected boundary = , and sutures ∈ , we can compute the sutured Floer homology () from the bordered invariant ()(). The chain complex (,) defining is quasi-isomorphic to the derived tensor product ()x() where _() () is a module associated to .
In the other direction we give a description of the bordered invariants in terms of sutured Floer homology. If F is a closed connected surface, then the bordered algebra () is a direct sum of certain sutured Floer complexes. These correspond to the 3-manifold ( \ ²;)×[0,1], where the sutures vary in a finite collection. Similarly, if is a connected 3-manifold with boundary = , the module ()_() is a direct sum of sutured Floer complexes for where the sutures on d vary over a finite collection. The multiplication structure on () and the action of () on () correspond to a natural gluing map on sutured Floer homology. (Further work of the author shows that this map coincides with the one defined by Honda, Kazez, and Matic, using contact topology and open book decompositions)
Immersed Floer homology of satellites
No full textLagrangian Floer theory is one of the main tools of current research in symplectic geometry. In immersed Lagrangian Floer homology, the differential counts rigid holomorphic disks with Lagrangian boundary condition associated with the immersion. We focused on the rigidity condition of holomorphic disks and visualized it as the angle change of the image, applied this result to computations of immersions of S¹ into S². In particular, we computed the immersed Floer homology of (1, 3) and (1, 4)-satellite knots of S¹ using this result and some other techniques, and found a general expression of the Floer homology of (p, q)-satellite knots of S¹.Ph.D.Includes bibliographical reference
Skein relations for tangle Floer homology
No full textIn a previous paper, V\'ertesi and the first author used grid-like Heegaard
diagrams to define tangle Floer homology, which associates to a tangle a
differential graded bimodule . If is obtained
by gluing together , then the knot Floer homology
of can be recovered from . In the present paper, we prove
combinatorially that tangle Floer homology satisfies unoriented and oriented
skein relations, generalizing the skein exact triangles for knot Floer
homology.Comment: 72 pages, 48 figures, 5 tables. Minor revision
Contact handles, duality, and sutured Floer homology
No full textWe give an explicit construction of the Honda–Kazez–Matić gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link Floer homology defined by the first author via sutured manifold cobordisms and by the second author via elementary cobordisms agree
Homological actions on sutured Floer homology
No full textWe define the action of the homology group H_1(M,∂M) on the sutured Floer homology SFH(M,γ). It turns out that the contact invariant EH(M,γ,ξ) is usually sent to zero by this action. This fact allows us to refine an earlier result proved by Ghiggini and the author. As a corollary, we classify knots in #^n(S^1×S^2) which have simple knot Floer homology groups: They are essentially the Borromean knots. This answers a question of Ozsváth.
In a different direction, we show that the only links in S^3 with simple knot Floer homology groups are the unlinks
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