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Kervaire Problems in Stable Homotopy Theory

Ch. 12. P. 189–236.
Akhmetiev Petr M.

The Kervaire Problem in Stable Homotopy Theory is a problem to classify framed immersions with Arf-invariant one. The first interesting example is in dimension 30. There exists a closed stably-parallelizable manifold ˜M 30
\protect\tilde{M}^{ with Arf–Kervaire invariant 1. The goal of the chapter is to recall various geometrical constructions concerning the Kervaire Problem. In particular, we give a self-contained description of the Mahowald element in the stable homotopy group of spheres 2l \varPi_{2^l}., l ≥ 3l \ge 3.. Using this construction, we prove that the Generalized Kervaire Problem, formulated by the author in Akhmetiev (Kervaire Problems in Stable Homotopy Theory (2016). arXiv:1608.01206v1 [math.AT]), is solved positively.

Language: English
Full text
DOI
Keywords: immersionпогружение

In book

Essays on Topology Dedicated to Valentin Poénaru
Akhmet’ev P. Switzerland: Springer, 2025.
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