论文标题
通过对应关系的双变量代数恢复
A bi-variant algebraic cobordism via correspondences
论文作者
论文摘要
为A对$（x，y）$定义的双变量理论$ \ mathbb b（x，y）$是一种与富尔顿的属性相似的理论，与富尔顿 - 麦克弗森的bivariant理论$ \ mathbb b（x \ x \ xrightArrow f y）$定义了用于hormphism $ f：x x \ y $ $。在本文中，使用信函构建了双变量的代数$ω^{*，\ sharp}（x，y）$，以至于$ω^{*，\ sharp}（x，pt）$是lee-pandharipande的eLgebraic cobord $ $ y_____________________________*尤其是，$ω^{*}（x，pt）=ω^{*，0}（x，pt）$是levine的同构 - - 莫雷尔的代数cobordism $ω__{ - *}（x）$。也就是说，$ω^{*，\ sharp}（x，y）$是\ emph {lee--pandharipande的bi-variant vesion} bungebraic bungerbaic bundles $ω_ {*，\ sharp}（x）$。
A bi-variant theory $\mathbb B(X,Y)$ defined for a pair $(X,Y)$ is a theory satisfying properties similar to those of Fulton--MacPherson's bivariant theory $\mathbb B(X \xrightarrow f Y)$ defined for a morphism $f:X \to Y$. In this paper, using correspondences we construct a bi-variant algebraic cobordism $Ω^{*,\sharp}(X, Y)$ such that $Ω^{*,\sharp}(X, pt)$ is isomorphic to Lee--Pandharipande's algebraic cobordism of vector bundles $Ω_{-*,\sharp}(X)$. In particular, $Ω^{*}(X, pt)=Ω^{*, 0}(X, pt)$ is isomorphic to Levine--Morel's algebraic cobordism $Ω_{-*}(X)$. Namely, $Ω^{*,\sharp}(X, Y)$ is \emph{a bi-variant vesion} of Lee--Pandharipande's algebraic cobordism of bundles $Ω_{*,\sharp}(X)$.
