CYLINDRICAL CONTACT HOMOLOGY OF A DEHN TWIST

2009 ◽  
Vol 20 (12) ◽  
pp. 1479-1525
Author(s):  
MEI-LIN YAU

We use open book representations of contact 3-manifolds to compute the cylindrical contact homology of a Stein-fillable contact 3-manifold represented by the open book whose monodromy is a positive Dehn twist on a torus with boundary.

2016 ◽  
Vol 187 (1) ◽  
pp. 17-67 ◽  
Author(s):  
Tetsuya Ito ◽  
Keiko Kawamuro
Keyword(s):  

2015 ◽  
Vol 26 (03) ◽  
pp. 1550027 ◽  
Author(s):  
Tetsuya Ito ◽  
Keiko Kawamuro

Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whose fractional Dehn twist coefficients greater than one for all the boundary components supports a tight contact structure.


2006 ◽  
Author(s):  
Pooja K. Agarwal ◽  
Jeffrey D. Karpicke ◽  
Sean H. Kang ◽  
Henry L. Roediger ◽  
Kathleen B. McDermott

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan

The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.


Buildings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 260
Author(s):  
James Ellis ◽  
David John Edwards ◽  
Wellington Didibhuku Thwala ◽  
Obuks Ejohwomu ◽  
Ernest Effah Ameyaw ◽  
...  

This research explores the failure of competitively tendered projects in the UK construction industry to procure the most suited contractor(s) to conduct the works. Such work may have equal relevance for other developed nations globally. This research seeks to teach clients and their representatives that “lowest price” does not mean “best value”, by presenting a case study of a successfully negotiated tender undertaken by a small-to-medium enterprise (SME) contractor; SME studies are relatively scant in academic literature. By applying the “lessons learnt” principle, this study seeks to improve future practice through the development of a novel alternative procurement option (i.e., negotiation). A mixed philosophical stance combining interpretivism and pragmatism was used—interpretivism to critically review literature in order to form the basis of inductive research to discuss negotiation as a viable procurement route, and pragmatism to analyse perceptions of tendering and procurement. The methods used follow a three-stage waterfall process including: (1) literature review and pilot study; (2) quantitative analysis of case study data; and (3) qualitative data collection via a focus group. Our research underscores the need to advise clients and their representatives of the importance of understanding the scope of works allowed within a tender submission before discounting it based solely on price. In addition, we highlight the failings of competitive tendering, which results in increased costs and project duration once the works commence on site. These findings provide new contemporary insight into procurement and tendering in the construction industry, with emphasis on SME contractors, existing relationships, and open-book negotiation. This research illustrates the adverse effects of early cost estimates produced without first securing a true understanding of project buildability and programming. Our work concludes with a novel insight into an alternative procurement option that involves early SME contractor involvement in an open-book environment, without the need for a third-party cost control.


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