Note on the Cyclotomic Polynomial Topologically

Abstract

Coefficients of the cyclotomic polynomial can be interpreted topologically, as the torsion in the homology of a certain simplicial complex associated with the degree of the cyclotomic polynomial, which was studied by Musiker and Reiner. We answer a question posed by the two authors regarding homotopy type of certain subcomplexes of the associated simplicial complex when the degree of the cyclotomic polynomial is a product of three distinct primes.

Keywords:

• Cyclotomic polynomial
• simplicial complexes
• homotopy type
• fundamental group

Subject Classification Codes:

• 05E45
• 55P15
• 57M05

Acknowledgments

The authors would like to thank Goran Djanković for drawing their attention to the paper [1]. The authors also thank the anonymous referee for the careful reading of the original version and useful suggestions for improvement of a presentation of results.

Declaration of Interest

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and the thrid author are partially supported by Ministry of Education, Science and Technological Development of Republic of Serbia Project #174032.