On H-spaces and a Congruence of Catalan Numbers

Authors

Tamar Friedmann, Smith CollegeFollow
John Harper, University of Rochester

Document Type

Article

Publication Date

2017

Publication Title

Homology, Homotopy and Applications

Abstract

For p an odd prime and F the cyclic group of order p, we show that the number of conjugacy classes of embeddings of F in SU(p) such that no element of F has 1 as an eigenvalue is (1 + C_p−1)/p, where C_p−1 is a Catalan number. We prove that the only coset space SU(p)/F that admits a p-local H-structure is the classical Lie group PSU(p). We also show that SU(4)/Z₃, where Z₃ is embedded off the center of SU(4), is a novel example of an H-space, even globally. We apply our results to the study of homotopy classes of maps from BF to BSU(n).

Volume

19

Issue

2

First Page

21

Last Page

30

DOI

dx.doi.org/10.4310/HHA.2017.v19.n2.a2

Recommended Citation

Friedmann, Tamar and Harper, John, "On H-spaces and a Congruence of Catalan Numbers" (2017). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/75