Kairvaire Problems in Stable Homotopy Theory

2016/08/03 by Петр Михайлович Ахметьев, Akhmet'ev, Petr
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1608.01206

Abstract

The Kervaire Problem is an unsolved problem in Stable Homotopy Theory. The first interesting example is in dimension 30. There exists a closed stably-parallelizable manifold M³⁰ with Arf-Kervaire invariant 1. It is unknown, if such a manifold exists in dimension 126? The goal of the paper is to recall the construction of the manifold M³⁰ and investigate its properties.

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