• 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 (5,324 words) - 04:57, 24 June 2025
  • 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)...
    11 KB (1,810 words) - 09:48, 26 June 2025
  • 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 (1,582 words) - 14:33, 8 December 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 (1,858 words) - 20:42, 3 March 2025
  • 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) - 00:30, 13 June 2025
  • 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
  • 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, 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
  • 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 (433 words) - 05:47, 27 May 2025
  • homeomorphism, respectively), the s-cobordism theorem states that if the manifolds are not simply-connected, an h-cobordism is a cylinder if and only if the...
    12 KB (1,906 words) - 11:00, 13 June 2025
  • 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 (1,983 words) - 11:32, 23 June 2025
  • 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 (7,049 words) - 20:46, 13 January 2025
  • comes from studying a hypothetical cobordism between this boundary and a sphere, and showing this hypothetical cobordism invalidates certain properties of...
    2 KB (191 words) - 13:28, 4 February 2025
  • 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...
    83 KB (8,124 words) - 04:10, 28 March 2025
  • Thumbnail for Genus of a multiplicative sequence
    equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the property that...
    14 KB (2,718 words) - 06:56, 11 April 2024
  • 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) - 17:30, 2 May 2025
  • Brown–Peterson cohomology BP is a summand of MU(p), which is complex cobordism MU localized at a prime p. In fact MU(p) is a wedge product of suspensions...
    4 KB (451 words) - 22:19, 2 November 2023
  • 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 (2,186 words) - 17:01, 12 June 2025
  • between layers of a cake Dental restoration Symplectic filling, a kind of cobordism in mathematics Part of the leather crusting process Fill (disambiguation)...
    351 bytes (81 words) - 20:05, 26 May 2019
  • 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 (2,809 words) - 05:35, 24 April 2025
  • 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) - 06:29, 14 April 2025
  • 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 (7,553 words) - 10:43, 28 March 2025
  • 7
    Zbl 1460.55017. Sloane, N. J. A. (ed.). "Sequence A001676 (Number of h-cobordism classes of smooth homotopy n-spheres.)". The On-Line Encyclopedia of Integer...
    29 KB (2,747 words) - 19:53, 14 June 2025
  • cork is that when attempting to use the h-cobordism theorem in four dimensions, the cork is the sub-cobordism that contains all the exotic properties of...
    5 KB (659 words) - 12:01, 17 May 2025
  • Thumbnail for Topology
    Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...
    38 KB (4,367 words) - 12:44, 29 June 2025
  • 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 (787 words) - 09:00, 22 June 2025
  • Thumbnail for Lev Pontryagin
    as one of the co-founders of cobordism theory, and co-discoverers of the central idea of this theory, that framed cobordism and stable homotopy are equivalent...
    12 KB (1,032 words) - 17:50, 26 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...
    25 KB (3,662 words) - 20:54, 2 June 2025
  • are not assumed to be simply connected, then an h-cobordism need not be a cylinder. The s-cobordism theorem, due independently to Mazur, Stallings, and...
    77 KB (10,647 words) - 03:27, 4 May 2025