CW-공간의 쐐기합의 호모토피 국소화상의 가환 코곱에 관한 연구 = Commutative comultiplications on homotopy localizations of the wedge sum of CW-spaces

다국어 초록 (Multilingual Abstract)

In this paper, we study homotopy comultiplication and homotopy commutative comultiplication structures on the localized space. Using Whitehead products and Hopf-Hilton invariants, we investigate the structure of homotopy comultiplications and develop some conditions for homotopy comultiplications to be commutative up to homotopy. Our results highlight the influence of the topological localizations at a collection of primes on the homotopical structures of co-Hopf spaces and extend existing studies on the wedge sum of spheres and Moore spaces to the localized counterparts.

목차 (Table of Contents)

• 1. Introduction 1
• 2. Preliminaries 5
• 2.1. Co-H-spaces 5
• 2.2. CW-complexes 7
• 2.3. Basic Whitehead products 8
• 3. Algebraic and topological localizations 17
• 3.1. Localizationｓ of abelian groups 17
• 3.2. Topological localizations 18
• 3.3. Notations and their fundamental properties 22
• 3.4. Notations for the topological localizations 32
• 4. Localized homotopy commutative comultiplications 36
• 4.1. Homotopy commutative conditions 36
• 4.2. Homotopy perturbations 39
• 4.3. Main results 61
• 5. Examples 68
• 5.1. Examples of homotopy commutative comultiplications 68
• 5.2. Table 73
• References 74
• 국문요약 76