标题： 余维一的Heegaard Floer不变量 显示英文标题

标题： Heegaard Floer invariants in codimension one

摘要： 使用Heegaard Floer同调论，我们为任何光滑的、定向的$4$-流形$X$构造了一个数值不变量，其同调与$S^1 \times S^3$相同。 Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. 我们展示如何利用这个不变量来阻碍某些类型的$3$-流形的嵌入，包括由有理同调$3$-球面与任意数量的$S^1 \times S^2$的连通和得到的流形。 我们还给出了在某些开放的$4$-流形中的类似阻碍条件，包括奇异的$\mathbb{R}^4$。 显示英文摘要

摘要： Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of certain types of $3$-manifolds, including those obtained as a connected sum of a rational homology $3$-sphere and any number of copies of $S^1 \times S^2$. We also give similar obstructions to embeddings in certain open $4$-manifolds, including exotic $\mathbb{R}^4$s.