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