Architecture of Infinite Towers and Skyscrapers

2021 ◽  
pp. 211-216
Author(s):  
Stefan Behrens ◽  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Quotient Space

Architecture of Towers and Skyscrapers formalizes the results from the previous chapter, regarding the structure of gropes and towers, and establishes the notation used for towers and skyscrapers in the remainder of the book. In particular, the boundaries of towers and skyscrapers are carefully described. The boundaries are divided into subsets called the floor, the walls, and the ceiling, and the topology of each of them is identified. The walls are associated with certain mixed Bing–Whitehead decompositions from a previous chapter. How the endpoint compactification of a tower corresponds to a quotient space with respect to a decomposition is also described.

The Collar Adding Lemma

2021 ◽  
pp. 391-394
Author(s):  
Daniel Kasprowski ◽  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Quotient Space ◽  
Embedding Theorem

The collar adding lemma is a key ingredient in the proof of the disc embedding theorem. Specifically, it proves that a skyscraper with an added collar is homeomorphic to the standard 4-dimensional 2-handle. The proof is similar to the proof in a previous chapter that the Alexander gored ball with an added collar is homeomorphic to the standard 3-ball. Roughly speaking, a skyscraper is seen as the quotient space of the 4-ball corresponding to a certain decomposition. The added collar allows the decomposition to be modified so that the resulting decomposition shrinks; that is, the corresponding quotient space, which is identified with the skyscraper with an added collar, is homeomorphic to the original 4-ball.

A Decomposition That Does Not Shrink

2021 ◽  
pp. 87-94
Author(s):  
Stefan Behrens ◽  
Christopher W. Davis ◽  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Quotient Space ◽  
Infinite Sequence ◽  
Embedding Theorem ◽  
Connected Components

‘A Decomposition That Does Not Shrink’ gives a nontrivial example of a decomposition of the 3-sphere such that the corresponding quotient space is not homeomorphic to the 3-sphere. The decomposition in question is called the Bing-2 decomposition. Similar to the Bing decomposition from the previous chapter, it consists of the connected components of the intersection of an infinite sequence of nested solid tori. However, unlike the Bing decomposition, the Bing-2 decomposition does not shrink. This indicates the subtlety of the question of which decompositions shrink. The question of when certain decompositions of the 3-sphere shrink is central to the proof of the disc embedding theorem.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Capitalising upon Globalisation

2018 ◽  
Author(s):  
David M. Webber
Keyword(s):  
Political Economy ◽  
Foreign Policy ◽  
International Development ◽  
Macroeconomic Policy ◽  
Domestic Policy ◽  
Policy Decisions ◽  
Gordon Brown ◽  
Development Policies ◽  
At Home

Having mapped out in the previous chapter, New Labour’s often contradictory and even ‘politically-convenient’ understanding of globalisation, chapter 3 offers analysis of three key areas of domestic policy that Gordon Brown would later transpose to the realm of international development: (i) macroeconomic policy, (ii) business, and (iii) welfare. Since, according to Brown at least, globalisation had resulted in a blurring of the previously distinct spheres of domestic and foreign policy, it made sense for those strategies and policy decisions designed for consumption at home to be transposed abroad. The focus of this chapter is the design of these three areas of domestic policy; the unmistakeable imprint of Brown in these areas and their place in building of New Labour’s political economy. Strikingly, Brown’s hand in these policies and the themes that underpinned them would again reappear in the international development policies explored in much greater detail later in the book.

Barking Up the Wrong Trees

2018 ◽  
Author(s):  
Michael Goodhart
Keyword(s):  
Global Economy ◽  
Power Relations ◽  
Normative Theory ◽  
Global Order ◽  
The Poor ◽  
Scope Of Justice ◽  
Principles Of Justice ◽  
Ideological Context

This chapter shows that three of the central debates within global normative theory are afflicted by the three pathologies associated with the dominant approach. Constructivist methods for identifying principles of justice are both blatantly undemocratic and severely distortional; debates about the scope of justice are depoliticizing, question begging, and philosophically irresolvable; claims about how the global order affects the poor depoliticize and distort power relations in the global economy and ignore the ideological context in which the claims themselves operate. The argument is not that IMT gives problematic answers to these questions but rather that the questions themselves are unhelpful and unnecessary, artifacts of the approach. In making these arguments, the chapter continues the work of defamiliarization begun in the previous chapter.

Ronald Coase and the Difference between Markets and Firms

2018 ◽  
Author(s):  
Abraham A. Singer
Keyword(s):  
Transaction Cost ◽  
Economic Activity ◽  
Transaction Cost Economics ◽  
Theory Of The Firm ◽  
Tabular Form ◽  
Specific Investment ◽  
The Difference ◽  
Marginal Revolution ◽  
The Way

This chapter reviews the development of transaction cost economics and unpacks its theory of the firm. The chapter begins with the marginal revolution in economics and how it altered the way economists understood the corporation. It then reviews the work of Ronald Coase and Oliver Williamson, explaining how they provided a novel account of firms. Transaction cost economics emphasizes how firms use hierarchy and bureaucracy to overcome problems of opportunism and asset-specific investment to coordinate some types of economic activity more efficiently than markets can. The transaction cost account of the corporation’s productivity component is shown in tabular form in comparison with its historical forerunners reviewed in the previous chapter.

Buying with You, Selling with You, Praying with You

2017 ◽  
Author(s):  
Stefania Tutino
Keyword(s):  
Market Economy ◽  
Catholic Church ◽  
Social Economic ◽  
Catholic Theology ◽  
Religious Traditions ◽  
Social Views ◽  
Cultural Reality ◽  
The Relationship

This chapter presents a second case study showing another concrete example of the issues to which probabilism was applied. Like the previous chapter, this chapter puts the theoretical and theological discussions on probabilism into the concrete social, economic, and cultural reality of the post-Reformation Catholic Church. This chapter explores the relationship between Catholic theology and money lending by examining the key role that probabilism played in helping theologians to maintain the traditional Catholic ban on usury while at the same time engaging with the burgeoning money-market economy and with other religious traditions with different doctrinal and social views on money, such as Judaism.

Further Implications of the Augmented Production Functions

2018 ◽  
Author(s):  
John H. Pencavel
Keyword(s):  
Production Functions ◽  
Full Time ◽  
Part Time ◽  
Relative Productivity

In this chapter, the author uses the output–hours findings presented in the previous chapter to interpret the research on the relative productivity of part-time and full-time workers. Examples are given of prior research that corroborate the author’s findings. Additionally, the productivity of hours of overtime are considered. Finally, the author applies the theory to macroeconomics.

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