Academic literature on the topic 'Whitney and Thom stratifications'

This chapter discusses the definition of admissible variations of mixed Hodge structure (VMHS), the results of M. Kashiwara in A study of variation of mixed Hodge structure (1986), and applications to the proof of algebraicity of the locus of certain Hodge cycles. It begins by recalling the relations between local systems and linear differential equations as well as the Thom–Whitney results on the topological properties of morphisms of algebraic varieties. The definition of a VMHS on a smooth variety is given, and the singularities of local systems are discussed. The chapter then studies the p

In colonial towns—settlements founded or developed by Western, imperial powers—two or more ‘cities’ usually exist: ‘the indigenous, ‘‘tradition-orientated’’ settlement, frequently manifesting the characteristics of the ‘‘pre-industrial city’’, and on the other hand, the ‘‘new’’ or ‘‘western’’ city, established as a result of the colonial process’ (King 1976: 5–6). But Caribbean cities gainsay this duality. Caribbean societies have virtually no pre- European inhabitants, and the non-Western elements in their cultures are no more indigenous than the traits of their white elites. Caribbean cities are quintessentially colonial, products of early mercantilism. Their creole (local or American) cultural characteristics were fashioned in the Caribbean by white sugar planters, merchants, and administrators who enslaved the blacks they imported from Africa, and with them bred a hybrid group—the free coloured people (Braithwaite 1971). Caribbean colonial cities are characterized by a morphological unity imposed by Europeans, yet their social and spatial structures have been compartmentalized by these creole social divisions (Clarke 1975a; Goodenough 1976; Welch 2003) Caribbean societies have been moulded by colonialism, the sugar plantation and slavery. These historical factors have also been underpinned by insularity, which facilitated occupation, exploitation, and labour control— and implicated port cities in such seaborne activities as sugar export and slave-labour recruitment. Accordingly, four themes provide the organizational framework for this chapter on Kingston, the principal city of Jamaica, during the colonial period: the economy, population, colour-class-culture stratification, and the spatial aspects of the city’s organization. The themes relate to different scales: the urban economy expresses the global aspects of commercial transactions; population and race-class stratification refer to the juxtaposition of different populations and cultures within colonial society; these socio-economic structures give rise to distinctive spatial configurations within the urban community. By 1800 Kingston was the major city and port of the largest British colony in the Caribbean, and its multiracial population was rigidly stratified into legal estates. Since the early nineteenth century, Jamaica has experienced a sequence of clearly identified historical events—slave emancipation in 1834, equalization of the sugar duties after 1845, a workers’ riot in 1938, and a slow process of constitutional decolonization after 1944, leading up to independence in 1962. This chapter is therefore organized around three major periods in Caribbean history—slavery (1692–1838), emancipation and the postemancipation period (1838–1944), and constitutional decolonization (1944– 62).

Chapter Three focuses on the tumultuous episode where Atlanta’s most vulnerable citizens, primarily poor black children, were being hunted and murdered. To clarify this, chapter three explores the experience of the victims’ families through oral interviews, the FBI papers, and archival research to show how the popular political sentiment of Atlanta’s black working classes and poor towards Atlanta’s black City Hall was one of distrust that thwarts the black Mecca image. Crucial to understanding the Atlanta Child Murders again notes that the prism of race was not the only lens to better understanding this convoluted community, but that class stratification within black Atlanta(s) are lucid. The Atlanta Child Murders provide a unique counter-narrative on class to Atlanta’s black Mecca status, as victims who were poor black youth were labeled and dismissed as “hustlers and runaways” in effect suggesting that they deserved what happened to them. Chapter three accounts for the experiences of the Committee to Stop Children’s Murder (STOP Committee) and the Techwood Bat Patrol, organizations formed by some of Atlanta’s black working class and poor as they deemed it necessary to organize against the murderers because to them, Jackson was too busy bolstering the black Mecca image while sacrificing Atlanta’s poor to play politics. This chapter grapples with the idea that at this time, Atlanta’s black political leadership was already working with Atlanta’s white business elite to host the 1988 Democratic National Convention and the 1996 Olympic Games. As a result, it was widely believed by a large segment of the public that Atlanta’s black City Administration downplayed the murders to show that social and economic progress had been made in the South and thus promoting a “city too busy to hate.” Just as important, many in black Atlanta felt that Williams was not the killer and that another killer remained on the loose.