JournalscmhVol. 72 , No. 3DOI 10.1007/s000140050028

Topology of complete intersections

  • F. Fang

    Nankai University, Tianjin, China
Topology of complete intersections cover

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+32{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+32{n+3}\over{2} , then Xn(d) and Xn(d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.