On the immersion problem for -torsion lens spaces

Building on the methods and results in [Bol. Soc. Mat. Mexicana (3) 9 (2003) 339; Shimkus, Immersions of 2-torsion lens spaces, Ph.D. Thesis, Lehigh University, 2002] we obtain some new nonimmersion results for 2 r -torsion lens spaces. In particular, we settle the immersion problem for those ( 2 n + 1 )-dimensional lens spaces with α ( n ) = 3 and n odd. The methods are based on the analysis of modified Postnikov towers for lifting the relevant stable normal bundles; Davis and Mahowaldʹs method [Proc. London Math. Soc. (3) 35 (1977) 333] for evaluating k-invariants plays a major role.