Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Mannan, Wajid"'
Autor:
Mannan, Wajid
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society Vol. 146 (2009), Issue 03, pp. 671-673
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 condition. We show that the two properties are in fact equivalent for all
Externí odkaz:
http://arxiv.org/abs/2310.07722
Autor:
Mannan, Wajid
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society Vol. 161 (2016), Issue 02, pp. 199-202
Gruenberg and Linnell showed that the standard relation module of a free product of $n$ groups of the form $C_r \times \mathbb{Z}$ could be generated by just $n+1$ generators, raising the possibility of a relation gap. We explicitly give such a set o
Externí odkaz:
http://arxiv.org/abs/2308.12930
Autor:
Mannan, Wajid, O'Shea, Seamus
Publikováno v:
Algebr. Geom. Topol. 13 (2013), Issue 6, pp. 3287-3304
We show that cancellation of free modules holds in the stable class $\Omega_3(\mathbb{Z})$ over dihedral groups of order $4n$. In light of a recent result on realizing $k$-invariants for these groups, this completes the proof that all all dihedral gr
Externí odkaz:
http://arxiv.org/abs/2308.12920
Autor:
Mannan, Wajid
Publikováno v:
Bulletin of the London Mathematical Society 40 (2008), Issue 4, pp. 664-674
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 fundamental group) finite of odd order, then the stable class of
Externí odkaz:
http://arxiv.org/abs/2308.12905
Autor:
Mannan, Wajid
Publikováno v:
Algebr. Geom. Topol. 7 (2007), Issue 1, pp. 517-528
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 fundamental group is dihedral of order $2^n$, and offer a complete solu
Externí odkaz:
http://arxiv.org/abs/2308.12897
Autor:
Mannan, Wajid
Publikováno v:
Homology, Homotopy and Applications Vol. 10 (2008), No. 2, pp. 135-137
We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.
Comment: Paper published in pe
Comment: Paper published in pe
Externí odkaz:
http://arxiv.org/abs/2401.03355
Autor:
Mannan, Wajid
Publikováno v:
Algebr. Geom. Topol. 9 (2009), Issue 3, pp. 1399-1411
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 finite group presentation. This reduces the D(2) problem to a questio
Externí odkaz:
http://arxiv.org/abs/2308.12541
Autor:
Mannan, Wajid
Publikováno v:
Homology, Homotopy and Applications Vol. 19 (2017), No. 1, pp. 171-179
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 notation one may express an even stronger version of Poincare duality for M
Externí odkaz:
http://arxiv.org/abs/2308.12390
Autor:
Mannan, Wajid
Publikováno v:
Homology, Homotopy and Applications Vol. 9 (2007), No. 2, pp. 445-449
We work over an arbitrary ring R. Given two truncated projective resolutions of equal length for the same module we consider their underlying chain complexes. We show they may be stabilized by projective modules to obtain a pair of complexes of the s
Externí odkaz:
http://arxiv.org/abs/2308.11871
Autor:
Mannan, Wajid
The realization problem asks: When does an algebraic complex arise, up to homotopy, from a geometric complex? In the case of 2- dimensional algebraic complexes, this is equivalent to the D2 problem, which asks when homological methods can distinguish
Externí odkaz:
http://arxiv.org/abs/2308.11844