6 research outputs found
Generalized Davis-Januszkiewicz spaces and their applications to algebra and topology
No full textNotbohm, D.R.A.W. [Promotor
Vector bundles over Davis-Januszkiewicz spaces with prescribed characteristic classes
No full textFor any (n - 1)-dimensional simplicial complex, we construct a particular n-dimensional complex vector bundle over the associated Davis- Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley Reisner algebra. We show that the isomorphism type of this complex vector bundle as well as of its realification are completely determined by its characteristic classes. This allows us to show that coloring properties of the simplicial complex are reflected by splitting properties of this bundle and vice versa. Similar questions are also discussed for 2n-dimensional real vector bundles with particular prescribed characteristic Pontrjagin and Euler classes. We also analyze which of these bundles admit a complex structure. It turns out that all these bundles are closely related to the tangent bundles of quasi-toric manifolds and moment angle complexes. © 2012 American Mathematical Society
Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces
No full textWe show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley-Reisner algebra of K. © 2009 The Author(s)
Homology decompositions for p-compact groups
No full textAbstractWe construct a homotopy theoretic setup for homology decompositions of classifying spaces of p-compact groups. This setup is then used to obtain a subgroup decomposition for p-compact groups which generalizes the subgroup decomposition with respect to p-stubborn subgroups for a compact Lie group constructed by Jackowski, McClure and Oliver
On Davis-Januszkiewicz homotopy types II: Completion and globalisation
No full textFor any finite simplicial complex K, Davis and Januszkiewicz defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to the original examples. It is therefore natural to investigate the extent to which the homotopy type of a space X is determined by such a cohomology ring. Having analysed this problem rationally in Part I, we here consider it prime by prime, and utilise Lannes' T -functor and Bousfield-Kan type obstruction theory to study the p-completion of X. We find the situation to be more subtle than for rationalisation, and confirm the uniqueness of the completion whenever K is a join of skeleta of simplices. We apply our results to the global problem by appealing to Sullivan's arithmetic square, and deduce integral uniqueness whenever the Stanley-Reisner algebra is a complete intersection
The classification of weighted projective spaces
No full textWe obtain two classifications of weighted projective spaces; up to homeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid
