Making lifting obstructions explicit

Link:
Autor/in:
Erscheinungsjahr:
2013
Medientyp:
Text
Schlagworte:
  • Differential
  • Bundle
  • Differential cohomology
  • Algebra
  • Category
  • Module
  • Differential
  • Bundle
  • Differential cohomology
  • Algebra
  • Category
  • Module
Beschreibung:
  • If P→X is a topological principal K-bundle and a central extension of K by Z, then there is a natural obstruction class in sheaf cohomology whose vanishing is equivalent to the existence of a -bundle over X with. In this paper, we establish a link between homotopy theoretic data and the obstruction class 1(P) which in many cases can be used to calculate this class in explicit terms. Writing for the connecting maps in the long exact homotopy sequence, two of our main results can be formulated as follows. If Z is a quotient of a contractible group by the discrete group Γ, then the homomorphism 3(X)→Γ induced by coincides with and if Z is discrete, then induces the homomorphism. We also obtain some information on obstruction classes defining trivial homomorphisms on homotopy groups. © 2012 London Mathematical Society.
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  • info:eu-repo/semantics/restrictedAccess
Quellsystem:
Forschungsinformationssystem der UHH
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Quelldatensatz
oai:www.edit.fis.uni-hamburg.de:publications/752f29c7-d73a-4ab4-b91f-85b3c47c2cf0