The main goal of this paper is to show that shellability is NP-hard for triangulated d-balls (this also gives hardness for triangulated d-manifolds/d-pseudomanifolds with boundary) as soon as d is at least 3. This extends our earlier work with Goaoc, Pat\'akov\'a and Wagner on hardness of shellability of 2-complexes and answers some questions implicitly raised by Danaraj and Klee in 1978 and explicitly mentioned by Santamar\'ia-Galvis and Woodroofe. Together with the main goal, we also prove that collapsibility is NP-hard for 3-complexes embeddable in the 3-space, extending an earlier work of the second author and answering an open question mentioned by Cohen, Fasy, Miller, Nayyeri, Peng and Walkington; and that shellability is NP-hard for 2-complexes embeddable in the 3-space, answering another question of Santamar\'ia-Galvis and Woodroofe (in a slightly stronger form than what is given by the main result).
翻译:本文的主要目的是表明,在三维空间内,三维拼凑的d-manfolds/d-superdomanani founds with border 至少3年之后,我们早期与Goaoc、Pat\'akov\a'a和Wagner就2个复合体的硬性可弹性开展的工作,延伸了我们以前与Goaoc、Pat\'akov\'a和Wagner就2个复合体的硬性弹性问题开展的工作,并回答了1978年Danaraj和Klee隐含的、Santamar\'ia-Galvis和Woodroofe明确提到的一些问题。 与主要目标一起,我们还证明3个空间内嵌入的3个复合体的3个复合体是硬化的。 第二作者的早期工作延长了,并回答了Cohen、Fasy、Miller、Nayeri、Peng和Walkington提到的一个开放问题;3个空间内嵌嵌入的2个复合体的2个复合体的可弹性是硬性NP-硬性,回答另一个Santamar\'ia-Galvis和Woodofe(比主要结果显示的形式稍强)。