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 (PDF). Princeton, NJ: Princeton Univ. Pr. ISBN 0-691-08191-3.
Topology of 4-Manifolds by Robion C. Kirby ISBN 0-387-51148-2