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.

See also

• Hauptvermutung

References

• Rudyak, Yuli B. (2001). "Piecewise linear structures on topological manifolds". arXiv:math.AT/0105047 [math.AT]. 
• Kirby, Robion C.; Siebenmann, Laurence C. (1977) (). Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton, NJ: Princeton Univ. Pr.. ISBN 0-691-08191-3. http://www.maths.ed.ac.uk/~aar/haupt/ks.pdf 
• Topology of 4-Manifolds by Robion C. Kirby ISBN 0-387-51148-2