PRESERVATION AND DISTORTION OF AREA IN FINITELY PRESENTED GROUPS

Authors
GERSTEN SM
Citation
Sm. Gersten, PRESERVATION AND DISTORTION OF AREA IN FINITELY PRESENTED GROUPS, Geometric and functional analysis, 6(2), 1996, pp. 301-345
Citations number
43
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Geometric and functional analysis → ACNP
ISSN journal
1016443X
Volume
6
Issue
2
Year of publication
1996
Pages
301 - 345
Database
ISI
SICI code
1016-443X(1996)6:2<301:PADOAI>2.0.ZU;2-9
Abstract
If K = G x phi Z where phi is a tame automorphism of the 1-relator gro up, G, then the combinatorial area of loops in a Cayley graph of G is undistorted in a Cayley graph of K. Examples of distortion or area in fibres of fibrations over the circle given and a notion of exponent of area distortion is introduced and studied. The inclusion of a finitel y generated abelian subgroup in the fundamental group of a compact 3-m anifold does not distort area.