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In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of ...
There are several possibilities; see the book by Hirsch. What is usually understood by Thom's transversality theorem is a more powerful statement about jet transversality. See the books by Hirsch and by Golubitsky and Guillemin. The original reference is Thom, Bol. Soc. Mat. Mexicana (2) 1 (1956), pp. 59–71.
In mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini.
The Free High School Science Texts (FHSST) organization is a South African non-profit project, which creates open textbooks on scientific subjects. Textbooks are edited to follow the government's syllabus, and published under a Creative Commons license (CC BY [1]), allowing teachers and students to print them or share them digitally.
The embedded manifold together with the isomorphism class of the normal bundle actually encodes the same information as the cobordism class []. This can be shown [ 2 ] by using a cobordism W {\displaystyle W} and finding an embedding to some R N W + n × [ 0 , 1 ] {\displaystyle \mathbb {R} ^{N_{W}+n}\times [0,1]} which gives a homotopy class ...
"High school physics textbooks" (PDF). Reports on high school physics. American Institute of Physics; Zitzewitz, Paul W. (2005). Physics: principles and problems. New York: Glencoe/McGraw-Hill. ISBN 978-0078458132
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.
:Used concepts developed in the then-current textbooks (e.g., vector analysis and non-Euclidean geometry) to provide entry into mathematical physics with a vector-based introduction to quaternions and a primer on matrix notation for linear transformations of 4-vectors. The ten chapters are composed of 4 on kinematics, 3 on quaternion methods ...