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Lectures on the Geometry of Manifolds, 2020
Description: The three higher-dimensional versions of the fundamental theorem of calculus – Green's theorem, the divergence theorem, and Stokes' theorem – that one encounters in a typical multi-variable calculus course have two paradoxical ...
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Description: The three higher-dimensional versions of the fundamental theorem of calculus – Green's theorem, the divergence theorem, and Stokes' theorem – that one encounters in a typical multi-variable calculus course have two paradoxical ...
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Contemporary Trends in Algebraic Geometry and Algebraic Topology
, 2002Mathematics in the 20th Century (M Atiyah) The [PHI]4 of Minimal Gorenstein 3-Folds of General Type (M Chen) Morphisms of Curves and the Fundamental Group (M Cushman) Iterated Integrals and Algebraic Cycles: Examples and Prospects (R Hain) Chen's ...
S. Chern, Lei Fu, R. Hain
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Algebraic topology : an intuitive approach
, 1999Objectives Homeomorphisms and homotopy equivalences Topological spaces and cell complexes Fundamental groups and higher homotopy groups Homology Homology groups of cell complexes Cohomology Homology of product spaces and the universal coefficient theorem
佐藤 肇
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THEORY OF I * -FUNCTOR IN ALGEBRAIC TOPOLOGY——REAL TOPOLOGY OF FIBER SQUARES
, 1975Mathematics has for its objects of study space forms and quantitative relations in the exteriorworld. For algebraic topology in particular, the space forms involved are the various kinds oftopological spaces.
Wu Wen-tsun
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, 1970 Riemann Surfaces and Algebraic Curves: A First Course in Hurwitz Theory
, 2016Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the ...
R. Cavalieri, Eric Miles
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An algebraic topological perspective to privacy
American Control Conference, 2016We cast the classic problem of achieving k-anonymity for a given database as a problem in algebraic topology. Using techniques from this field of mathematics, we propose a framework for k-anonymity that brings new insights and algorithms to anonymize a ...
A. Speranzon, S. Bopardikar
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Differential forms in algebraic geometry – A new perspective in the singular case
, 2016Differential forms are a rich source of invariants in algebraic geometry. This approach was very successful for smooth varieties, but the singular case is less wellunderstood.
Annette Huber-Klawitter
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The principle of topological economy in algebraic geometry
2005This part of the lecture is not related to the first part, so it can be understood independently. We start with an example. Example 1. In ℂP n , consider two algebraic varieties X and Y of complementary dimensions. In general position, they intersect in finitely many points. Let [ X ] and [ Y ] be the homology classes realized by the varieties
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Геометрия центральных расширений нильпотентных алгебр Ли
Труды Математического института имени В. А. Стеклова, 2019Предложен рекуррентный и монотонный способ построения и классификации нильпотентных алгебр Ли путем последовательных центральных расширений. Он заключается в вычислении вторых когомологий $H^2(\mathfrak g,\mathbb K)$ расширяемой нильпотентной алгебры Ли $\mathfrak g$ с последующим изучением геометрии пространства орбит действия группы автоморфизмов ...
Dmitry Vladimirovich Millionshchikov +1 more
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