Premium
A Note on the Nilpotency of Subgroups of Self‐Homotopy Equivalences
Author(s) -
Félix Yves,
Murillo Aniceto
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003020
Subject(s) - mathematics , homotopy , n connected , homotopy sphere , homotopy category , homotopy group , regular homotopy , cofibration , pure mathematics , classifying space , group (periodic table) , bott periodicity theorem , whitehead theorem , combinatorics , algebra over a field , chemistry , organic chemistry
Let X be a space that has the homotopy type of a finite simply connected CW complex. We denote by E ( X ) the group of homotopy classes of self‐homotopy equivalences of X . This group has been extensively studied (see [ 1 ] for a survey). In this paper we consider the subgroup E n # ( X ) consisting of homotopy classes of self‐homotopy equivalences of X that induce the identity on the homotopy groups π i ( X ) for i ⩽ n , and the subgroup E # ( X ) consisting of homotopy classes of self‐homotopy equivalences of X that induce the identity on all the homotopy groups. Our first result is as follows. 1991 Mathematics Subject Classification 55P62, 55P10.