hausdorff-center for mathematics

Papers and Publications

  • Signature theorem for orbifolds revisited.

    In this paper we give a new proof the signature theorem for orbifolds using the cobordism techniques developed in previous papers.
  • Hochschild cohomology and string topology of global quotient orbifolds. (with B.Uribe and E. Backelin). .pdf

Let M be a connected, simply connected, closed and oriented manifold and G a nite group acting on M by orientation preserving di eomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the orbifold [M/G] and the Hochschild cohomology of the dg-ring obtained by performing the smash product between the group G and the singular cochain complex of M. As an application we obtain a description of the string topology of manifolds with finite fundamental group in terms of Hochschild cohomology.

  • Orbifold cobordism. .pdf

    In this paper we undertake the study of different cobordism rings of orbifolds, our main results present decompositions of the unoriented cobordism ring of orbifolds with isotropy groups of odd order, and the rational oriented cobordism ring; these rings are expresed in terms of bordism rings of classifying spaces of the Weyl group of a finite subgroup of O(n).
  • When is a manifold the boundary of an orbifold? .pdf

    The aim of this short communication is to review some classical results on cobordism of manifolds and discuss recent extensions of this theory to orbifolds. In particular, we give an answer to the question, When is a manifold the boundary of an orbifold? in the oriented case and in the unoriented case when we restrict to isotropy groups of odd order.
  • A spectral sequence for orbifold cobordism .pdf

    The aim of this paper is to introduce a spectral sequence that converges to the cobordism groups of orbifolds with given isotropy representations. We use this spectral sequence to calculate some cobordism groups of orbifolds for low dimensions.>



Last modified: March 25th, 2012.