We prove a basic inequality for the $d$-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors. As a corollary, a degree one map between two aspherical Seifert homology spheres is homotopic to a homeomorphism if and only if the Heegaard Floer homologies are isomorphic.

中文翻译：

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Heegaard Floer同源性和拼接同源性球

我们证明了同源球中一系列结的$ d $不变量的基本不等式。结果，我们能够在Seifert纤维同源球体之间的映射下证明减少的Floer同源性等级上的新关系，从而改善了第一作者和第二作者的结果。推论是，当且仅当Heegaard Floer同源性是同构的时，两个非球面Seifert同源球之间的一个度图才是同胚的同位。