(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)...

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

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

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

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...

(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...

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

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...

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...

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"...

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...

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...

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

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

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...

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

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

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...

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

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...

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...

(To prove this result, Lev Pontryagin developed the concept of framed cobordism.) If f , g : X → S p {\displaystyle f,g\colon X\to S^{p}} has ‖ f ( x...

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...

theorem Signature (topology) Handle decomposition Handlebody h-cobordism theorem s-cobordism theorem Manifold decomposition Hilbert-Smith conjecture Mapping...

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...

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...

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 Theory of Computation Continuum...