22 citations · 48 across the 7 of their papers we have counts for
6 papers · 1 filter
Realizing algebraic 2-complexes by cell complexes
Wajid Mannan
The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness con…
Minimal algebraic complexes over
Wajid Mannan, Seamus O'Shea
We show that cancellation of free modules holds in the stable class over dihedral groups of order . In light of a recent result on realizing -invariants fo…
The third homotopy module of a 2-complex
Wajid Mannan
Given a connected 2-complex X with fundamental group G, we show how pi_3(X) may be computed as a module over Z[G]. Further we show that if X is a finite connected 2-complex with G…
The D(2) property for
Wajid Mannan
Wall's D(2) problem asks if a cohomologically 2-dimensional geometric 3-complex is necessarily homotopy equivalent to a geometric 2-complex. We solve part of the problem when the f…
Quillen's Plus Construction and the D(2) problem
Wajid Mannan
Given a finite connected 3-complex with cohomological dimension 2, we show it may be constructed up to homotopy by applying the Quillen plus construction to the Cayley complex of a…
Duality in the homology of 5-manifolds
Wajid Mannan
We show that the homological properties of a 5-manifold M with fundamental group G are encapsulated in a G-invariant stable form on the dual of the third syzygy of Z. In this notat…