This is a review essay of Angus Fletcher’s posthumous The Topological Imagination: Spheres, Edges, and Islands (2016). Fletcher’s guiding intuition is that topology—a vast, foundational, formally rigorous pillar of modern mathematics—can offer fresh, useful ways of seeing and thinking about our world. These novel modes of perception and cognition are, Fletcher contends, naturally anticipated by literary creation and theories of it—hence the book’s title, The Topological Imagination. Half of my essay is consequently devoted to fleshing out the larger contexts of Fletcher’s investigation: topology’s core concepts, Romantic theories of the imagination, and earlier encounters between topology and literary and philosophical thought, particularly that of Blanchot and Deleuze. The other half of this essay asks whether Fletcher’s accounts of topology and the (Romantic) imagination are accurate and compatible, and what true compatibility might look like. To answer this final question, I turn to recent debates about form and formalization and A. R. Ammons’s book-length poem, Sphere: The Form of a Motion (1974).

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