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The groups of self‐homotopy equivalences and the Tits alternative
Author(s) -
Maruyama Kenichi
Publication year - 2011
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/blms/bdr053
Subject(s) - mathematics , homotopy , rank (graph theory) , homotopy group , pure mathematics , group (periodic table) , algebra over a field , combinatorics , chemistry , organic chemistry
In this paper, we study the group of self‐homotopy equivalences. We prove a theorem that is analogous to Tits' well‐known theorem for linear groups. Using this result, we determine a condition for the group of self‐homotopy equivalences to be of finite rank.