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 , 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 . Furthermore, we prove that, if d has no prime factors less than , 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. 466–480DOI 10.1007/S000140050028