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2 results

  • THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS

  • Part of
  • ANDREW STACEY
  • Journal:
    Glasgow Mathematical Journal / Volume 59 / Issue 1 / January 2017
    Published online by Cambridge University Press:
    10 June 2016, pp. 27-59
    Print publication:
    January 2017
    • Article
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  • We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite-dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the action of the diffeomorphism group of the circle. It is not a useful action on the manifold that we define. We consider how one might fix this problem and conclude that it can only be done by completing to the space of loops of bounded variation.

  • The rational topology of gauge groups and of spaces of connections

  • Svjetlana Terzić
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 1 / January 2005
    Published online by Cambridge University Press:
    01 December 2004, pp. 262-270
    Print publication:
    January 2005
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  • Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this paper we give explicit formulas for the rational homotopy groups and cohomology algebra of the gauge group and of the space of (irreducible) connections modulo gauge transformations for any such bundle.