(1968). Notes on cobordism theory. Princeton, NJ: Princeton University Press. While every cobordism is a cospan, the category of cobordisms is not a "cospan...
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differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence)...
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functors of the cobordism category and the objects of C {\displaystyle {\mathcal {C}}} . Symmetric monoidal functors from the cobordism category correspond...
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In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally...
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List of cohomology theories (redirect from Unoriented cobordism ring)
derived. Cobordism studies manifolds, where a manifold is regarded as "trivial" if it is the boundary of another compact manifold. The cobordism classes...
14 KB (1,976 words) - 21:48, 25 September 2024
In mathematics, the oriented cobordism ring is a ring where elements are oriented cobordism classes of manifolds, the multiplication is given by the Cartesian...
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Handle decomposition (section Cobordism presentations)
(m,k)-handlebody of genus g . A handle presentation of a cobordism consists of a cobordism W where ∂ W = M 0 ∪ M 1 {\displaystyle \partial W=M_{0}\cup...
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Thom space (section Real cobordism)
encodes the same information as the cobordism class [ M ] {\displaystyle [M]} . This can be shown by using a cobordism W {\displaystyle W} and finding an...
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In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a field. It was introduced by Marc Levine...
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hyperbolic pair of pants as described above, and all are obtained as such). A cobordism between two n-dimensional closed manifolds is a compact (n+1)-dimensional...
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semi-s-cobordism if (and only if) the inclusion M ↪ W {\displaystyle M\hookrightarrow W} is a simple homotopy equivalence (as in an s-cobordism), with...
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with Fabien Morel, the theory of algebraic cobordism, an algebraic-geometry analog of the theory of cobordism in algebraic topology. In 2002, he was an...
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Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...
35 KB (4,041 words) - 16:11, 3 October 2024
comes from studying a hypothetical cobordism between this boundary and a sphere, and showing this hypothetical cobordism invalidates certain properties of...
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topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds by considering...
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Homotopy groups of spheres (section Framed cobordism)
true.[citation needed] Homotopy groups of spheres are closely related to cobordism classes of manifolds. In 1938 Lev Pontryagin established an isomorphism...
82 KB (7,977 words) - 00:48, 18 September 2024
Swampland (physics) (section Cobordism conjecture)
can be violated via a dynamical process. This intuition leads to the cobordism conjecture. Consider a gravitational theory that can be put on two backgrounds...
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rings arises in this way. For example, the Lazard ring is the ring of cobordism classes of complex manifolds. A graded-commutative ring with respect to...
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Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...
14 KB (2,250 words) - 15:44, 24 August 2024
essential ingredient of the proof of the Smale h-cobordism theorem, and its generalization to the s-cobordism theorem. A manifold is called a "k-handlebody"...
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oriented cobordism M S O ∗ ( X ) , {\displaystyle MSO^{*}(X),} complex cobordism M U ∗ ( X ) , {\displaystyle MU^{*}(X),} and so on. Complex cobordism has...
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boundary of the cobordism has dimension 4 (as shown by Donaldson). If the cobordism has dimension 4, then it is unknown whether the h-cobordism theorem holds...
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Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...
42 KB (5,730 words) - 13:52, 26 September 2024
Atiyah–Singer index theorem (section Cobordism)
on manifolds with boundary. Their first published proof replaced the cobordism theory of the first proof with K-theory, and they used this to give proofs...
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copy of X {\displaystyle X} itself at infinity. The resulting space is a cobordism between X {\displaystyle X} and a disjoint union of n ( Q ) {\displaystyle...
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four. Building on these works, he also established the more powerful h-cobordism theorem the following year, together with the full classification of simply-connected...
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Anomaly (physics) (section Anomalies and cobordism)
Liouville action In the modern description of anomalies classified by cobordism theory, the Feynman-Dyson graphs only captures the perturbative local...
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International Congress of Mathematicians in Edinburgh for the foundations of cobordism theory, which were already present in his thesis. He was invited speaker...
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Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...
23 KB (4,312 words) - 18:07, 6 September 2024
theorem Signature (topology) Handle decomposition Handlebody h-cobordism theorem s-cobordism theorem Manifold decomposition Hilbert-Smith conjecture Mapping...
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