9 citations · 20 across the 6 of their papers we have counts for
5 papers · 1 filter
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…
A fake Klein bottle with bubble
Wajid Mannan
We resolve the question of the existence of a finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble, but homotopically distinct…