Kirby–Siebenmann class

Kirby–Siebenmann class

In mathematics, the Kirby–Siebenmann class is an element of the fourth cohomology group:e(M) in H^4(M;mathbf{Z}_2)which must vanish if a topological manifold "M" is to have a piecewise linear structure. It is named for Robion Kirby and Larry Siebenmann.

ee also

*Hauptvermutung

References

*cite arXiv|author=Yuli B. Rudyak|title=Piecewise linear structures on topological manifolds|year=2001|version=|eprint=math.AT/0105047
*citation|url=http://www.maths.ed.ac.uk/~aar/haupt/ks76.pdf |title=Foundational Essays on Topological Manifolds, Smoothings, and Triangulations|first= Robion C. |last=Kirby|first2= Laurence C.|last2=Siebenmann |year=1977|ISBN= 0-691-08191-3
*"Topology of 4-Manifolds" by Robion C. Kirby ISBN 0-387-51148-2


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Laurent C. Siebenmann — Laurent Carl Siebenmann (the first name is sometimes spelled Laurence or Larry) (*1939 in Toronto) is a mathematician at the Université de Paris Sud at Orsay, France, who works on manifolds and who co discovered the Kirby Siebenmann class. He… …   Wikipedia

  • List of mathematics articles (K) — NOTOC K K approximation of k hitting set K ary tree K core K edge connected graph K equivalence K factor error K finite K function K homology K means algorithm K medoids K minimum spanning tree K Poincaré algebra K Poincaré group K set (geometry) …   Wikipedia

  • Piecewise linear manifold — In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise… …   Wikipedia

  • Obstruction theory — In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. Contents 1 In homotopy theory 2 In geometric topology 3 In surgery theory …   Wikipedia

  • Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… …   Wikipedia

  • Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

  • Differential structure — In mathematics, an n dimensional differential structure (or differentiable structure) on a set M makes M into an n dimensional differential manifold, which is a topological manifold with some additional structure that allows us to do differential …   Wikipedia

  • Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… …   Wikipedia

  • Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”