Browsing by Subject "singularity"
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Item Broken Lefschetz fibrations on smooth four-manifolds(2010-05) Williams, Jonathan Dunklin; Gompf, Robert E., 1957-; Etnyre, John B.; Luecke, John; Reid, Alan; Sadun, Lorenzo A.It is known that an arbitrary smooth, oriented four-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken Lefschetz fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken Lefschetz fibration in a given homotopy class of smooth maps. One notable application is that adding an additional projection move generates all broken Lefschetz fibrations, regardless of homotopy class. The paper ends with further applications and open problems.Item Koj?ve and Levinas: Universality Without Totality(2010-07-14) Pepitone, Anthony J.I have structured my master's thesis in terms of an opposition between Kojeve's existentialist, Marxist philosophical formulation of Hegel's Phenomenology and Levinas's post-Heideggerian, anti-Hegelian phenomenology in Totality and Infinity. While Levinas's project is explicitly anti-totalitarian, Kojeve's reading of the Phenomenology emphasizes the End of History in Hegel's philosophy without shrinking from its totalizing aspects. While the philosophical project of each thinker is generally antithetical to the other, it is my contention that the universal and homogeneous state, conceived by Kojeve to be the rational realization of the end of history, is a legitimate moral project for Levinasian ethics. This thesis provides both an exegesis of Kojeve's reading of Hegel's master/slave dialectic in the Phenomenology and an interpretation of the tragedy of the slave understood in terms of Holderlin's theory of the tragic. It is through the master/slave dialectic that history consummates in the end of history. Later in the thesis, I outline Levinas's project as an ethics as first philosophy in opposition to the Eleatic traditions in Western philosophy. We can trace Levinas's project in his unconventional reading of the cogito and the idea of infinity. Whereas Descartes represents a philosophical return home for Hegel, Levinas's reading of Descartes represents a philosophical sojourn away from home in the second movement of the Meditations. With these notions, we have a formal basis in accounting for the conflict in Levinas's thought between the moral necessity of universal rights and the dangers of assimilation. Finally, I argue for why the universal and homogeneous state is an ethically worthy goal from a Levinasian perspective. On this question, I engage the thought of a number of thinkers of the left: Kojeve, Derrida, Horkheimer, Adorno and Zizek. I conclude that Levinas's thought on universalism and eschatology can serve as a moral basis for the left-Hegelian project of realizing a universal and homogeneous state. Because such a state is distinguishable from a totalizing End of History, the eschatological concern for one's singularity within history is compatible with the prophetic call to strive for political universality. Ultimately, it is the responsibility to this prophetic call that guarantees one's singularity.