(1968). Notes on cobordism theory. Princeton, NJ: Princeton University Press. While every cobordism is a cospan, the category of cobordisms is not a "cospan...

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)...

functors of the cobordism category and the objects of C {\displaystyle {\mathcal {C}}} . Symmetric monoidal functors from the cobordism category correspond...

In mathematics, the oriented cobordism ring is a ring where elements are oriented cobordism classes of manifolds, the multiplication is given by the Cartesian...

In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally...

derived. Cobordism studies manifolds, where a manifold is regarded as "trivial" if it is the boundary of another compact manifold. The cobordism classes...

In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a field. It was introduced by Marc Levine...

(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...

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...

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...

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...

comes from studying a hypothetical cobordism between this boundary and a sphere, and showing this hypothetical cobordism invalidates certain properties of...

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...

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...

topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds by considering...

Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...

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...

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...

true.[citation needed] Homotopy groups of spheres are closely related to cobordism classes of manifolds. In 1938 Lev Pontryagin established an isomorphism...

Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...

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...

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...

oriented cobordism M S O ∗ ( X ) , {\displaystyle MSO^{*}(X),} complex cobordism M U ∗ ( X ) , {\displaystyle MU^{*}(X),} and so on. Complex cobordism has...

Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...

International Congress of Mathematicians in Edinburgh for the foundations of cobordism theory, which were already present in his thesis. He was invited speaker...

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...

Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...

Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism Metrics and properties Euler characteristic Betti number Winding number...

Liouville action In the modern description of anomalies classified by cobordism theory, the Feynman-Dyson graphs only captures the perturbative local...

theory Chaos theory Character theory Choquet theory Class field theory Cobordism theory Coding theory Cohomology theory Complex function theory Complexity...