Noncommutative deformation and a topological nature of singularity Koiter

TL;DR

This paper develops a model of noncommutative plastic deformation and demonstrates that Koiter's singularities have topological origins, specifically related to Pontryagin numbers, linking deformation theory with topology.

Contribution

It introduces a noncommutative deformation model and proves Koiter's hypothesis connecting singularities to topological invariants, a novel insight in the field.

Findings

Koiter's singularities are topologically rooted.

The number of Koiter singularities equals a Pontryagin topological number.

A new model of noncommutative plastic deformation is proposed.

Abstract

In this paper we constructed the model of noncommutative plastic deformation and give the proof of hypothesis Koiter. We showed, that occurrence of singularity Koiter has the topological reasons and number of singularities Koiter - it is topological number Pontriagin.