• Thumbnail for Cobordism
    (1968). Notes on cobordism theory. Princeton, NJ: Princeton University Press. While every cobordism is a cospan, the category of cobordisms is not a "cospan...
    34 KB (5,214 words) - 05:31, 10 May 2024
  • 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)...
    12 KB (1,882 words) - 17:14, 30 July 2024
  • functors of the cobordism category and the objects of C {\displaystyle {\mathcal {C}}} . Symmetric monoidal functors from the cobordism category correspond...
    3 KB (412 words) - 03:56, 27 March 2024
  • In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally...
    12 KB (1,579 words) - 01:24, 23 April 2024
  • 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...
    2 KB (250 words) - 16:39, 26 March 2024
  • Thumbnail for Handle decomposition
    (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...
    10 KB (1,855 words) - 03:12, 8 March 2024
  • 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...
    13 KB (1,978 words) - 18:32, 31 July 2024
  • In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a field. It was introduced by Marc Levine...
    3 KB (364 words) - 10:01, 13 December 2023
  • Thumbnail for Pair of pants (mathematics)
    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...
    12 KB (1,711 words) - 11:54, 3 December 2023
  • 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...
    4 KB (428 words) - 01:29, 24 June 2022
  • Thumbnail for Marc Levine (mathematician)
    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...
    4 KB (373 words) - 20:14, 17 June 2023
  • Thumbnail for Topology
    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...
    2 KB (185 words) - 04:02, 6 January 2021
  • Thumbnail for Differential topology
    topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds by considering...
    15 KB (1,837 words) - 18:20, 27 July 2023
  • Thumbnail for Homotopy groups of spheres
    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
  • 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...
    17 KB (2,531 words) - 03:36, 9 August 2024
  • 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...
    41 KB (5,655 words) - 15:25, 12 December 2023
  • Thumbnail for Interior (topology)
    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
  • Thumbnail for Handlebody
    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"...
    5 KB (785 words) - 11:35, 21 January 2023
  • oriented cobordism M S O ∗ ( X ) , {\displaystyle MSO^{*}(X),} complex cobordism M U ∗ ( X ) , {\displaystyle MU^{*}(X),} and so on. Complex cobordism has...
    44 KB (6,888 words) - 18:24, 2 October 2024
  • 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...
    15 KB (1,954 words) - 15:10, 3 August 2024
  • Thumbnail for General topology
    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
  • 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...
    53 KB (7,529 words) - 04:31, 30 May 2024
  • 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...
    8 KB (1,244 words) - 22:33, 19 September 2024
  • Thumbnail for Stephen Smale
    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...
    23 KB (2,160 words) - 19:36, 22 May 2024
  • Thumbnail for Anomaly (physics)
    Liouville action In the modern description of anomalies classified by cobordism theory, the Feynman-Dyson graphs only captures the perturbative local...
    21 KB (2,814 words) - 06:48, 22 August 2023
  • Thumbnail for René Thom
    International Congress of Mathematicians in Edinburgh for the foundations of cobordism theory, which were already present in his thesis. He was invited speaker...
    15 KB (1,356 words) - 19:05, 18 August 2024
  • 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...
    3 KB (262 words) - 12:17, 30 October 2023