75 research outputs found

    A Duality Exact Sequence for Legendrian Contact Homology

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    We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact homology CH_* which maps to singular homology. In particular, the sequence implies a duality between the kernel of the map (CH_*\to H_*) and the cokernel of the map (H_* \to CH^*). Furthermore, this duality is compatible with Poincare duality in L in the following sense: the Poincare dual of a singular class which is the image of a in CH_* maps to a class \alpha in CH^* such that \alpha(a)=1. The exact sequence generalizes the duality for Legendrian knots in Euclidean 3-space [24] and leads to a refinement of the Arnold Conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [6].Comment: 57 pages, 10 figures. Improved exposition and expanded analytic detai

    Invariants of Legendrian Knots and Coherent Orientations

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    We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knots in the standard contact R^3 and a relative version of Eliashberg and Hofer's Contact Homology. We use this translation to transport the idea of ``coherent orientations'' from the Contact Homology world to Chekanov's combinatorial setting. As a result, we obtain a lifting of Chekanov's differential graded algebra invariant to an algebra over Z[t,t^{-1}] with a full Z grading.Comment: 32 pages, 17 figures; small technical corrections to proof of Thm 3.7 and example 4.

    The Minimal Length of a Lagrangian Cobordism between Legendrians

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    To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a 11-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

    A 15-Year Analysis of Early and Late Autologous Hematopoietic Stem Cell Transplant in Relapsed, Aggressive, Transformed, and Nontransformed Follicular Lymphoma

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    AbstractAutologous stem cell transplant (ASCT) has been shown to be an effective treatment for follicular lymphoma (FL). We explored our experience in ASCT for FL among all patients treated over a 15-year period from diagnosis through their entire treatment history including relapse post ASCT. All patients who underwent an unpurged ASCT for relapsed, advanced FL between June 1990 and December 2000 were analyzed. After salvage therapy they received melphalan/etoposide/total body irradiation, BCNU, etoposide, cytarabine, melphalan (BEAM), or cyclophosphamide BCNU etoposide (CBV) as conditioning for the ASCT. One hundred thirty-eight patients with a median age of 48 years and a median follow-up of 7.6 years were analyzed. The majority were of the subtype grade 1, nontransformed (FL-NT), having had 1 prior chemotherapy. The progression-free (PFS) and overall survival (OS) of the FL-NT at 10 years were 46% and 57%, respectively, and at 5 years for the transformed (FL-T) were 25% and 56%, respectively, of which only the PFS was significantly different (P = .007). The median OS from diagnosis was 16 years for the FL-NT. ASCT positively altered the trend of shorter remissions with subsequent chemotherapies, and there was no difference in OS between those who had 1, 2, or >2 chemotherapies prior to ASCT. Salvage therapy for relapse post ASCT was effective (OS >1 year) in a third of patients. Unpurged ASCT is an effective tool in the treatment of relapsed, aggressive FL-NT and FL-T, is superior to retreatment with standard chemotherapy, is effective at various stages of treatment, is likely to have a beneficial influence on the natural history of this disease, and the disease is amenable to salvage therapy post-ASCT relapse

    Transplant Physicians’ Attitudes on Candidacy for Allogeneic Hematopoietic Cell Transplantation (HCT) in Older Patients: The Need for a Standardized Geriatric Assessment (GA) Tool

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    Background Despite improvements in conditioning regimens and supportive care having expanded the curative potential of HCT, underutilization of HCT in older adults persists (Bhatt VR et al, BMT 2017). Therefore, we conducted a survey of transplant physicians (TP) to determine their perceptions of the impact of older age (≥60 years) on HCT candidacy and utilization of tools to gauge candidacy. Methods We conducted a 23-item, online cross-sectional survey of adult physicians recruited from the Center for International Blood and Marrow Transplant Research between May and July 2019. Results 175/770 (22.7%) TP completed the survey; majority of respondents were 41-60 years old, male, and practicing in a teaching hospital. Over 75% were at centers performing ≥50 HCT per year. When considering regimen intensity, most (96%, n=168) had an upper age limit (UAL) for using a myeloablative regimen (MAC), with only 29 physicians (17%) stating they would consider MAC for patients ≥70 years. In contrast, when considering a reduced intensity/non-myeloablative conditioning (RIC/NMA), 8%, (n=13), 54% (n=93), and 20% (n=35) stated that age 70, 75, and 80 years respectively would be the UAL to use this approach, with 18% (n=31) reporting no UAL. TP agreed that Karnofsky Performance Score (KPS) could exclude older pts for HCT, with 39.1% (n=66), 42.6% (n=72), and 11.4% (n=20) requiring KPS of ≥70, 80, and 90, respectively. The majority (n=92, 52.5%) indicated an HCT-comorbidity index threshold for exclusion, mostly ranging from ≥3 to ≥ 5. Almost all (89.7%) endorsed the need for a better health assessment of pre-HCT vulnerabilities to guide candidacy for pts ≥60 with varied assessments being utilized beyond KPS (Figure 1). However, the majority of centers rarely (33.1%) or never (45.7%) utilize a dedicated geriatrician/geriatric-oncologist to assess alloHCT candidates ≥60 yrs. The largest barriers to performing GA included uncertainty about which tools to use, lack of knowledge and training, and lack of appropriate clinical support staff (Figure 2). Approximately half (n=78, 45%) endorsed GA now routinely influences candidacy. Conclusions The vast majority of TP will consider RIC/NMA alloHCT for patients ≥70 years. However, there is heterogeneity in assessing candidacy. Incorporation of GA into a standardized and easily applied health assessment tool for risk stratification is an unmet need. The recently opened BMT CTN 1704 may aid in addressing this gap

    Historical Archaeologies of the American West

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