On J. H. C. Whitehead's aspherical question I |
| |
Authors: | Joe Brandenburg Micheal Dyer |
| |
Institution: | (1) George Mason University, 22030 Fairfax, Virginia;(2) University of Oregon, 97403 Eugene, Oregon |
| |
Abstract: | A connected, finite two-dimensional CW-complex with fundamental group isomorphic toG is called a G, 2]
f
-complex. LetL⊲G be a normal subgroup ofG. L has weightk if and only ifk is the smallest integer such that there exists {l
1,…,l
k}⊆L such thatL is the normal closure inG of {l
1,…,l
k}. We prove that a G, 2]
f
-complexX may be embedded as a subcomplex of an aspherical complexY=X∪{e
1
2
,…,e
k
2
} if and only ifG has a normal subgroupL of weightk such thatH=G/L is at most two-dimensional and defG=defH+k. Also, ifX is anon-aspherical G, 2]
f
-subcomplex of an aspherical 2-complex, then there exists a non-trivial superperfect normal subgroupP such thatG/P has cohomological dimension ≤2. In this case, any torsion inG must be inP. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|