Dr Wajid Mannan
Lecturer in Mathematics
Email: w.mannan@qmul.ac.uk
Telephone: +44 (0)20 7882 5497
Room Number: Queens’ Building, Room E302A
Profile
Wajid has mostly worked in low dimensional topology on a family of conjectures centred around Wall's D(2) problem, which asks if it is possible to have a space (specifically a finite cell complex) which is homologically 2 dimensional, but geometrically 3 dimensional (in the sense that it is not homotopy equivalent to a space of lower dimension). Other aspects of low dimensional topology that he has worked on include computation of homotopy modules over the fundamental group and finding additional symmetries in the Poincare duality of manifolds.
Much of the algebra used to study these topological problems may be translated to other areas of mathematics and in particular he has done work on the Ktheory of cyclotomic fields, and the Borel regulator. Another direction he has worked in is finding closed model category structures for certain coalgebras and Lie algebras and exploring a unification of Koszul and Morita dualities.
He is currently studying quaternion group representations on lattices in relation to Wall's D(2) problem and applications of knot theory to helping robots deal with tangled cables. He is also interested in pursuing certain lines of thought concerning topological quantum field theory and exotic R4's.
Research
Research Interests:
Homotopy theory (of cell complexes), representation theory of groups (over Z), quandles, surgery on manifolds, kinvariants over integral group rings, Clifford algebras, Hochschild homology, MC elements, Ktheory over cyclotomic fields, Khovanov homology, closed model categories, topological quantum field theories, group presentations.
Publications

MANNAN WH (2017). Duality in the homology of 5manifolds. nameOfConference

MANNAN WH, Chuang J, Lazarev A (2016). KoszulMorita Duality. nameOfConference

MANNAN WH, Chaung J, Lazarev A (2016). COCOMMUTATIVE COALGEBRAS: HOMOTOPY THEORY AND KOSZUL DUALITY. nameOfConference

Mannan WH (2016). Explicit generators for the relation module in the example of GruenbergLinnell. nameOfConference

MANNAN WH, SanchezGarcia RJ, Snaith VP et al. (2015). Computing Borel’s regulator. nameOfConference

Mannan WH, O¿Shea S (2013). Minimal algebraic complexes over D4n. nameOfConference

Mannan WH (2013). A commutative version of the group ring. nameOfConference

Mannan WH (2009). Quillen's plus construction and the D(2) problem. nameOfConference

MANNAN WH (2009). Realizing algebraic 2complexes by cell complexes. nameOfConference

MANNAN WH (2008). The third homotopy module of a 2complex. nameOfConference

Mannan WH (2007). Homotopy types of truncated projective resolutions. nameOfConference