# Topology of complete intersections

### F. Fang

Nankai University, Tianjin, China

## Abstract

Let Xn(d) and Xn(d') be two n-dimensional complete intersections with the same total degree d. In this paper we prove that, if n is even and d has no prime factors less than ${n+3}\over{2}$ , then Xn(d) and Xn(d') are homotopy equivalent if and only if they have the same Euler characteristics and signatures. This confirms a conjecture of Libgober and Wood [16]. Furthermore, we prove that, if d has no prime factors less than ${n+3}\over{2}$ , then Xn(d) and Xn(d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.

## Cite this article

F. Fang, Topology of complete intersections. Comment. Math. Helv. 72 (1997), no. 3, pp. 466–480

DOI 10.1007/S000140050028