Abstract:
Let $\Delta_n$ be the simplicial complex of squarefree positive integers less than or equal to $n$ ordered by divisibility. It is known that the asymptotic rate of growth of its Euler characteristic is closely related to deep properties of the prime number system, such as the Prime Number Theorem and the Riemann Hypothesis.

The talk will be about the asymptotic growth behavior of the individual Betti numbers $\beta_k(\Delta_n)$ and of their sum. Also, a cell complex will be discussed whose cell inclusion relation models that of divisibility of all numbers upp to $n$, not only the squarefree ones.

The talk will be quite general and elementary, assuming no specialized background.