CORE
🇺🇦
make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Research partnership
About
About
About us
Our mission
Team
Blog
FAQs
Contact us
Community governance
Governance
Advisory Board
Board of supporters
Research network
Innovations
Our research
Labs
Vector bundles over Davis-Januszkiewicz spaces with prescribed characteristic classes
Authors
D.R.A.W. Notbohm
Publication date
1 January 2012
Publisher
'American Mathematical Society (AMS)'
Doi
Abstract
For 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
Similar works
Full text
Open in the Core reader
Download PDF
Available Versions
NARCIS
See this paper in CORE
Go to the repository landing page
Download from data provider
Last time updated on 14/10/2017
VU Research Portal
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:research.vu.nl:publication...
Last time updated on 18/04/2020