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1. |
Record Nr. |
UNINA9911015871303321 |
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Autore |
Mrozek Marian |
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Titolo |
Connection Matrices in Combinatorial Topological Dynamics / / by Marian Mrozek, Thomas Wanner |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
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ISBN |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (287 pages) |
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Collana |
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SpringerBriefs in Mathematics, , 2191-8201 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Dynamics |
Manifolds (Mathematics) |
Dynamical Systems |
Manifolds and Cell Complexes |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Preface -- Introduction -- Main Results -- Preliminaries -- Poset Filtered Chain Complexes -- Algebraic Connection Matrices -- Connection Matrices in Lefschetz Complexes -- Dynamics of Combinatorial Multivector Fields -- Connection Matrices for Forman's Gradient Vector Fields -- Future Work and Open Problems -- References. |
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Sommario/riassunto |
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This book provides an introduction to the theory of connection matrices in the context of combinatorial multivector fields. The theory of connection matrices was proposed by Conley and Franzosa for classical continuous-time dynamical systems as a tool for studying connecting orbits between isolated invariant sets. It generalizes the Morse complex in Morse theory, and has found numerous applications in dynamics. Connection matrices have been and still are a challenging topic to study, as there are no complete introductory texts, and both their intricate definition and properties are scattered over numerous research papers. In recent years, dynamical concepts have found their way into a combinatorial context. Starting with combinatorial vector fields, introduced by Forman to generalize classical Morse theory, it has been realized that this transfer of ideas can lead to important applications. Similarly, Conley's theory of isolated invariant sets has |
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been transferred to the combinatorial setting. This, when combined with the concept of multivector fields, opens the door to a complete combinatorial dynamical theory. In this book, we take Conley's theory one step further, by presenting a complete discussion of connection matrices for combinatorial multivector fields. While some of the results in this book are based on known approaches, we show in a detailed way how they can be carried over to the case of multivector fields on general Lefschetz complexes. Along the way, we introduce notions which are new even in the classical setting, such as a formal approach to addressing the nonuniqueness of connection matrices, as well as mechanisms for comparing connection matrices even under poset changes. Finally, we show that specifically for the case of Forman's gradient combinatorial vector fields connection matrices are necessarily unique, and can be determined explicitly in a straightforward way. Focusing on the combinatorial theory of connection matrices has a number of advantages. On the one hand, many of the technical difficulties of the classical continuous-time dynamics situation are not present in the discrete combinatorial context. This allows us to provide a complete and informal introduction to the theory in the second section of the book. This in turn will enable the readers to construct and analyze their own examples easily. On the other hand, the complete theory, including the existence of connecting orbits in the combinatorial setting can be presented in detail, based on an explicit distinction between the algebraic and topological parts of the theory. In this way, it is our hope that this book will be an impetus for further knowledge transfer between dynamics and combinatorics, and even topological data analysis. This text is aimed at researchers in the fields of dynamics and topological data analysis, and it is suitable for advanced graduate students interested in applying connection matrix methods to their own studies. |
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2. |
Record Nr. |
UNINA9910956574703321 |
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Autore |
Shonkwiler Alison |
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Titolo |
The Financial Imaginary : Economic Mystification and the Limits of Realist Fiction / / Alison Shonkwiler |
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Pubbl/distr/stampa |
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Minneapolis, Minnesota ; ; London, [England] : , : University of Minnesota Press, , 2017 |
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©2017 |
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ISBN |
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Descrizione fisica |
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1 online resource (200 pages) |
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Disciplina |
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Soggetti |
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Economics and literature - United States - History - 20th century |
Capitalism and literature - United States - History - 20th century |
Realism in literature |
Finance in literature |
Money in literature |
American fiction - 20th century - History and criticism |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction: Representing financial abstraction in fiction -- Virtue unrewarded: financial character in the economic novel -- Reagonomic realisms: real estate, character, and crisis in Jane Smiley's Good faith -- Epic compensations: corporate totality in Frank Norris's The octopus and Richard Powers's Gain -- Financial sublime: virtual capitalism in Don DeLillo's Cosmopolis -- Liquid realisms: global asymmetry and mediation in Teddy Wayne's Kapitoil and Mohsin Hamid's How to get filthy rich in raising Asia -- Epilogue: Literary realism and finance capital. |
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Sommario/riassunto |
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As the world has been reshaped since the 1970s by neoliberalism and globalization, increasing financial abstraction has presented a new political urgency for contemporary writers. Globalized finance, the return to Gilded Age levels of inequality, and the emergence of new technologies pose a similar challenge to the one faced by American social realists a century ago: making the virtualization of capitalism |
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legible within the conventions of the realist novel. In The Financial Imaginary , Alison Shonkwiler reads texts by Richard Powers, Don DeLillo, Jane Smiley, Teddy Wayne, and Mohsin Hamid to examine how fiction confronts the formal and representational mystifications of the economic. As Shonkwiler shows, these contemporary writers navigate the social, moral, and class preoccupations of American "economic fiction" (as shaped by such writers as William Dean Howells, Henry James, Frank Norris, and Theodore Dreiser), even as they probe the novel's inadequacies to tell the story of an increasingly abstract world system. Drawing a connection from historical and theoretical accounts of financialization to the formal contours of contemporary fiction, The Financial Imaginary examines the persistent yet vexed relationship between financial representation and the demands of literary realism. It argues that the novel is essential to understanding our relation to the mystifications of abstraction past and present. |
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