THREE-CROSSED MODULES

被引：12

作者：

Arvasi, Z. ^{[1
]}

Kuzpinari, T. S. ^{[2
]}

Uslu, E. Oe. ^{[3
]}

机构：

[1] Osmangazi Univ, Dept Math & Comp Sci, Art & Sci Fac, Eskisehir, Turkey

[2] Aksaray Univ, Dept Math, Art & Sci Fac, Aksaray, Turkey

[3] Afyon Kocatepe Univ, Dept Math, Art & Sci Fac, Afyon, Turkey

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2009年 / 11卷 / 02期

关键词：

crossed module; 2-crossed module; simplicial group; Moore complex; SIMPLICIAL GROUPS; ALGEBRAIC MODELS; CROSSED-MODULES; HOMOTOPY-GROUPS; CATEGORIES; SPACES;

D O I：

10.4310/HHA.2009.v11.n2.a8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of a 3-crossed module, which extends the notions of a 1-crossed module (Whitehead) and a 2-crossed module (Conduche). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups having a Moore complex of length 3. We make explicit the relationship with the cat(3)-groups (Loday) and the 3-hypercomplexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.

引用

页码：161 / 187

页数：27

共 26 条

[1]

Akca I., 2002, Homology Homotopy Appl., V4, P43, DOI [10.4310/HHA.2002.v4.n1.a4, DOI 10.4310/HHA.2002.V4.N1.A4]

[2]

Arvasi Z, 2006, J HOMOTOPY RELAT STR, V1, P1

[3]

Arvasi Z., 1997, Theory Appl. Categories, V3, P1

[4]

Baues H.J., 1995, Handbook of Algebraic Topology, P1, DOI [10.1016/B978-0-444-81779-2.X5000-7,ncatlab.org/nlab/files/Baues-HomotopyTypes.pdf, DOI 10.1016/B978-0-444-81779-2.X5000-7,NCATLAB.ORG/NLAB/FILES/BAUES-HOMOTOPYTYPES.PDF]

[5]

BAUES HJ, 1991, DEGRUYTER EXP MATH, V2

[6]

Bourn D, 2007, CONTEMP MATH, V431, P105

[7]

BROWN R, 1989, P LOND MATH SOC, V59, P51

[8] VANKAMPEN THEOREMS FOR DIAGRAMS OF SPACES [J].

BROWN, R ;

LODAY, JL .

TOPOLOGY, 1987, 26 (03) :311-335

[9] GROUP-THEORETIC ALGEBRAIC MODELS FOR HOMOTOPY TYPES [J].

CARRASCO, P ;

CEGARRA, AM .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1991, 75 (03) :195-235

[10]

CARRASCO P, 1987, THESIS U GRANADA

← 1 2 3 →