In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
Boldly original and boundary defining, The Topological Imagination clears a space for an intellectual encounter with the shape of human imagining. Joining two commonly opposed domains, literature and mathematics, Angus Fletcher maps the imagination’s ever-ramifying contours and dimensions, and along the way compels us to re-envision our human existence on the most unusual sphere ever imagined, Earth.
Words and numbers are the twin powers that create value in our world. Poetry and other forms of creative literature stretch our ability to evaluate through the use of metaphors. In this sense, the literary imagination aligns with topology, the branch of mathematics that studies shape and space. Topology grasps the quality of geometries rather than their quantifiable measurements. It envisions how shapes can be bent, twisted, or stretched without losing contact with their original forms—one of the discoveries of the eighteenth-century mathematician Leonhard Euler, whose Polyhedron Theorem demonstrated how shapes preserve “permanence in change,” like an aging though familiar face.
The mysterious dimensionality of our existence, Fletcher says, is connected to our inhabiting a world that also inhabits us. Theories of cyclical history reflect circulatory biological patterns; the day-night cycle shapes our adaptive, emergent patterns of thought; the topology of islands shapes the evolution of evolutionary theory. Connecting literature, philosophy, mathematics, and science, The Topological Imagination is an urgent and transformative work, and a profound invitation to thought.
The concept of “flesh” in philosophical terms derives from the writings of Maurice Merleau-Ponty. This was the word he used to name the concrete realm of sentient bodies and life processes that has been eclipsed by the abstractions of science, technology, and modern culture. Topology, to conventional understanding, is the branch of mathematics that concerns itself with the properties of geometric figures that stay the same when the figures are stretched or deformed.
Topologies of the Flesh is an original blend of continental thought and mathematical imagination. Steven M. Rosen opens up a new area of philosophical inquiry: topological phenomenology. Through his unique application of qualitative mathematics, he extends the approaches of Merleau-Ponty and Heidegger so as to offer a detailed exploration of previously uncharted dimensions of human experience and the natural world.
Rosen’s unprecedented marriage of topology and phenomenology is motivated by the desire to help overcome the pervasive dualism of contemporary philosophy and Western culture at large. To carry this to completion, he must address his own dualistic stance as author. Challenging the author’s traditional posture of detachment and anonymity, Rosen makes his presence vividly felt in his final chapter, and his philosophical analysis is transformed into a living reality.
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