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Complexification of real cycles and the Lawson suspension theorem
Author(s) -
Teh Jyh-Haur
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm007
Subject(s) - mathematics , suspension (topology) , complexification , holomorphic function , pure mathematics , homotopy , variety (cybernetics) , space (punctuation) , equivalence (formal languages) , algebra over a field , mathematical analysis , computer science , statistics , operating system
The space of totally real r ‐cycles of a totally real projective variety is embedded into the space of complex r ‐cycles by complexification. The holomorphic taffy argument in the proof of Lawson's suspension theorem is proved by using Chow forms, and this proof gives an analogous result for totally real cycle spaces. The Sturm theorem is used to derive a criterion for a real polynomials of degree d to have d distinct real roots, and this criterion is used to prove the openness of some subsets of real divisors. This enables us to prove that the suspension map induces a weak homotopy equivalence between two enlarged spaces of totally real cycle spaces.