On some results of S. Abramyan and T. Panov

TL;DR

This paper provides an expository overview and clarification of key definitions and results related to the construction of simplicial complexes and their moment-angle complexes, originally presented by Abramyan and Panov.

Contribution

It offers a clearer, more concise presentation of the main definitions and Theorem 5.1 from the original work, enhancing understanding of the results.

Findings

Clarified the main definitions used in Abramyan and Panov's results.

Presented a shorter, clearer statement of Theorem 5.1.

Highlighted the non-triviality of certain homotopy classes in moment-angle complexes.

Abstract

This note is purely expository and is an extended version of math review to the paper [AP19]=arXiv:1901.07918v3 by S. Abramyan and T. Panov published in Proc. of Steklov Math. Inst. 305 (2019). The authors construct simplicial complexes for whose moment-angle complexes certain homotopy classes are non-trivial. I present in a shorter and clearer way the main definition and the statement of Theorem 5.1 from [AP19]. The clarification reveals that the main definition used in the statements of the main results is not given [AP19].