New Spaces in Mathematics: Volume 1: Formal and Conceptual ReflectionsMathieu Anel, Gabriel Catren After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines. |
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New Spaces in Mathematics: Formal and Conceptual Reflections Mathieu Anel,Gabriel Catren Limited preview - 2021 |
Common terms and phrases
action affine algebraic geometry algebraic topology apply associated axioms bundle called classical classifying closed cohomology colimits commutative complex condition connected consider construction context continuous corresponding covering defined definition denote dependent derived described diagram diffeology differential elements embedding equality equivalent etale example exists extension fact fiber field finite formal frame functions functor fundamental give given Grothendieck groupoid higher homotopy type idea identity important inclusion instance interpretation introduced Intuitively isomorphism limits locally logic logos look manifold Math mathematics means moduli morphism natural Note notion objects operations particular path points precisely present presheaf problem quotient Recall relation result ring satisfying scheme sense sheaf sheaves simplicial simply singular smooth stacks structure tangent theorem topoi topological space topology topos type theory unique universal usual values