Arithmetic Invariants of Simplicial Complexes
Keyword(s):
What invariants of a finite simplicial complex K can be computed solely from the values v0(K), V1(K), …, vi(K), … where Vi(K) is the number of i-simplexes of K? The Euler chracteristic χ(K) = Σ i (– 1)ivi(K) is a subdivision invariant and a homotopy invariant while the dimension of K is a subdivision invariant and homeomorphism invariant. In [3], Wall has shown that the Euler chracteristic is the only linear function to the integers that is a subdivision invariant. In this paper we show that the only subdivision invariants (linear or not) of K are the Euler characteristic and the dimension. More precisely we prove the following theorem.
2017 ◽
Vol 60
(3)
◽
pp. 470-477
◽
Keyword(s):
Keyword(s):
2012 ◽
Vol 55
(1)
◽
pp. 157-163
◽
Keyword(s):