实圈的复杂化与Lawson悬置定理
Complexification of real cycles and Lawson suspension theorem
摘要：
通过复化将全实射影簇的全实$r$ -圈空间嵌入到复$r$ -圈空间中。利用Chow形式给出了Lawson悬挂定理证明中的全纯Taffy变元的一个证明，并给出了全实循环空间中的一个类似结果。本文利用Sturm定理导出了实多项式$d$有$d$不同实根的一个判别准则，并利用它证明了某些实因子子集的开性.这使我们能够证明，悬挂映射诱导的两个全实循环空间的扩大空间之间的弱同伦等价。
英文摘要：
We embed the space of totally real $r$-cycles of a totally real projective variety into the space of complex $r$-cycles by complexification. We provide a proof of the holomorphic taffy argument in the proof of Lawson suspension theorem by using Chow forms and this proof gives us an analogous result for totally real cycle spaces. We use Sturm theorem to derive a criterion for a real polynomial of degree $d$ to have $d$ distinct real roots and use it 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.
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