Fukaya A∞-structures associated to Lefschetz fibrations. V

2021 ◽  
pp. 1-70
Author(s):  
Paul Seidel
Keyword(s):  
Fukaya Category ◽  
Lefschetz Fibrations ◽  
Direct Identification ◽  
Lefschetz Fibration

We (re)consider how the Fukaya category of a Lefschetz fibration is related to that of the fiber. The distinguishing feature of the approach here is a more direct identification of the bimodule homomorphism involved.

scholarly journals A NOTE ON LEFSCHETZ FIBRATIONS ON COMPACT STEIN 4-MANIFOLDS

2012 ◽  
Vol 14 (05) ◽  
pp. 1250035 ◽  
Author(s):  
SELMAN AKBULUT ◽  
M. FIRAT ARIKAN
Keyword(s):  
Alternative Proof ◽  
Lefschetz Fibrations ◽  
Lefschetz Fibration

Loi–Piergallini and Akbulut–Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the disk D2 with bounded fibers. In this note we give a more intrinsic alternative proof of this result.

scholarly journals A real open book not fillable by a real Lefschetz fibration

2014 ◽  
Vol 25 (04) ◽  
pp. 1450031
Author(s):  
Ferit Öztürk ◽  
Nermin Salepci
Keyword(s):  
Real Structure ◽  
Manifolds With Boundary ◽  
Open Book ◽  
Lefschetz Fibrations ◽  
Open Book Decompositions ◽  
Lefschetz Fibration

A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of a real structure. We prove that there is a real open book which cannot be filled by a real Lefschetz fibration, although it is filled by non-real Lefschetz fibrations.

scholarly journals Classification of Boundary Lefschetz Fibrations over the Disc

2018 ◽  
pp. 399-418
Author(s):  
Stefan Behrens ◽  
Gil R. Cavalcanti ◽  
Ralph L. Klaasse
Keyword(s):  
Single Component ◽  
Stable Structure ◽  
Complex Structures ◽  
Lefschetz Fibrations ◽  
Lefschetz Fibration ◽  
Generalized Complex Structures ◽  
Type Change ◽  
Generalized Complex

This chapter shows that a 4-manifold admits a boundary Lefschetz fibration over the disc if and only if it is diffeomorphic to S1×S3#nCP¯2,#mCP2#nCP¯2 or #m(S2×S2). Given the relation between boundary Lefschetz fibrations and stable generalized complex structures, the chapter concludes that the 4-manifolds S1×S3#nCP¯2,#(2m+1)CP2#nCP¯2 and #(2m+1)S2×S2 admit stable generalized complex structures whose type change locus has a single component and are the only 4-manifolds whose stable structure arises from boundary Lefschetz fibrations over the disc.

scholarly journals Products of pairs of Dehn twists and maximal real Lefschetz fibrations

2013 ◽  
Vol 210 ◽  
pp. 83-132
Author(s):  
Alex Degtyarev ◽  
Nermin Salepci
Keyword(s):  
Existence And Uniqueness ◽  
Modular Group ◽  
Lefschetz Fibrations ◽  
Dehn Twists ◽  
Lefschetz Fibration ◽  
Geometric Application

AbstractWe address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic.

scholarly journals Products of pairs of Dehn twists and maximal real Lefschetz fibrations

2013 ◽  
Vol 210 ◽  
pp. 83-132 ◽  
Author(s):  
Alex Degtyarev ◽  
Nermin Salepci
Keyword(s):  
Existence And Uniqueness ◽  
Modular Group ◽  
Lefschetz Fibrations ◽  
Dehn Twists ◽  
Lefschetz Fibration ◽  
Geometric Application

AbstractWe address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic.

scholarly journals Diagnostic accuracy of MALDI-TOF mass spectrometry for the direct identification of clinical pathogens from urine

Open Medicine ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 266-273
Author(s):  
Min Tang ◽  
Jia Yang ◽  
Ying Li ◽  
Luhua Zhang ◽  
Ying Peng ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Likelihood Ratio ◽  
Meta Analysis ◽  
Positive Likelihood Ratio ◽  
Negative Likelihood Ratio ◽  
Urine Samples ◽  
Direct Identification ◽  
Maldi Tof Ms ◽  
Maldi Tof ◽  
Tof Ms

AbstractMatrix-assisted laser desorption ionization time of flight mass spectrometry (MALDI-TOF MS) has become one of the most popular methods for the rapid and cost-effective detection of clinical pathogenic microorganisms. This study aimed to evaluate and compare the diagnostic performance of MALDI-TOF MS with that of conventional approaches for the direct identification of pathogens from urine samples. A systematic review was conducted based on a literature search of relevant databases. The pooled sensitivity, specificity, positive likelihood ratio (PLR), negative likelihood ratio (NLR) and area under the summary receiver operating characteristic (SROC) curve of the combined studies were estimated. Nine studies with a total of 3920 subjects were considered eligible and included in the meta-analysis. The pooled sensitivity was 0.85 (95% CI 0.79-0.90), and the pooled specificity was 0.93 (95% CI 0.82-0.97). The PLR and NLR were 11.51 (95% CI 4.53-29.26) and 0.16 (95% CI 0.11-0.24), respectively. The area under the SROC curve was 0.93 (95% CI 0.91-0.95). Sensitivity analysis showed that the results of this meta-analysis were stable. MALDI-TOF MS could directly identify microorganisms from urine samples with high sensitivity and specificity.

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