标题： 非可逆性与（超）流形、“半”类纤维丛和同伦的“半” analogs 显示英文标题

标题： Noninvertibility and ``Semi-'' Analogs of (Super) Manifolds, Fiber Bundles and Homotopies

摘要： 超对称最初包含了非可逆对象，但通常只处理可逆对象，并在一定程度上将其分解。 我们建议重新考虑这一假设，并尝试使用某种弱化可逆性条件来重新定义超流形、纤维丛和同伦等基本概念。 前缀“半-”反映了基础态射构成的相应半群的特性，该半群由已知的群部分和新的理想非可逆部分组成。 我们发现，缺乏可逆性以一种自然的方式为我们提供了超流形和纤维丛的转移函数的广义余循环条件，这可能导致非可逆的Čech余循环类比物的构造。 我们定义了半同伦，它可以是非可逆的，并描述映射到引入的半超流形的情况。 显示英文摘要

摘要： Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semi- reflects the fact that the underlying morphisms form corresponding semigroups consisting of a known group part and a new ideal noninvertible part. We found that the absence of invertibility gives us the generalization of the cocycle conditions for transition functions of supermanifolds and fiber bundles in a natural way, which can lead to construction of noninvertible analogs of \v{C}ech cocycles. We define semi-homotopies, which can be noninvertible and describe mappings into the semi-supermanifolds introduced.