Topology of complete intersections | Zendy

Fuquan Fang | Zendy

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Topology of complete intersections

Author(s) -

Fuquan Fang

Publication year - 1997

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050028

Subject(s) - mathematics , homotopy , euler characteristic , conjecture , prime (order theory) , combinatorics , pontryagin's minimum principle , degree (music) , euler's formula , topology (electrical circuits) , discrete mathematics , pure mathematics , mathematical analysis , physics , mathematical optimization , acoustics , optimal control

. Let X n (d) and X n (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 X n (d) and X n (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 , then X n (d) and X n (d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.

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