# Commentarii Mathematici Helvetici

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**Volume 72, Issue 3, 1997, pp. 466–480**

**DOI: 10.1007/s000140050028**

Published online: 1997-09-30

Topology of complete intersections

F. Fang^{[1]}(1) Nankai University, Tianjin, China

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.

*Keywords: *Complete intersection, homotopy equivalence, homeomorphism

Fang F.: Topology of complete intersections. *Comment. Math. Helv.* 72 (1997), 466-480. doi: 10.1007/s000140050028