LIE MODELS FOR THE COMPONENTS OF SECTIONS OF A NILPOTENT FIBRATION

被引：24

作者：

Buijs, Urtzi ^{[1
]}

Felix, Yves ^{[2
]}

Murillo, Aniceto ^{[3
]}

机构：

[1] Univ Malaga, Dept Matemat Aplicada, Malaga 29000, Spain

[2] Catholic Univ Louvain, Inst Math Pure & Appliquee, B-1348 Louvain, Belgium

[3] Univ Malaga, Dept Algebra Geometria & Topol, Malaga 29080, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 10期

关键词：

Space of sections; mapping space; Sullivan model; Quillen model; rational homotopy theory; RATIONAL HOMOTOPY-THEORY; SPACE;

D O I：

10.1090/S0002-9947-09-04870-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed mapping spaces. Among the applications presented, we obtain a Lie model of the exponential law and prove that, in many cases, the rank of the homotopy groups of the mapping space grows at the same rate as the rank of the homotopy groups of the target space.

引用

页码：5601 / 5614

页数：14

共 16 条

[1]

Bousfield A.K., 1976, Mem. Am. Math. Soc., V179

[2] On the rational homotopy type of function spaces [J].

Brown, EH ;

Szczarba, RH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (12) :4931-4951

[3]

BUIJS U, COMMENT MAT IN PRESS

[4] Basic constructions in rational homotopy theory of function spaces [J].

Buijs, Urtzi ;

Murillo, Aniceto .

ANNALES DE L INSTITUT FOURIER, 2006, 56 (03) :815-838

[5]

DASILVEIRA FEA, 1984, PAC J MATH, V113, P1

[6] RATIONAL CATEGORY OF THE SPACE OF SECTIONS OF A NILPOTENT BUNDLE [J].

FELIX, Y .

COMMENTARII MATHEMATICI HELVETICI, 1990, 65 (04) :615-622

[7]

FELIX Y, COMMENT MAT IN PRESS

[8] RATIONAL HOMOTOPY OF THE SPACE OF SECTIONS OF A NILPOTENT BUNDLE [J].

HAEFLIGER, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 273 (02) :609-620

[9]

Halperin S., 2001, GRAD TEXT M, V205, DOI 10.1007/978-1-4613-0105-9

[10]

HILTON P, 1975, N HOLLAND MATH STUDI, V15

← 1 2 →