Cobordism of maps on $Z_2$-Witt spaces

Jean-Paul Brasselet; Alice Kimie Miwa Libardi; Eliris Rizziolli; Marcelo Saia

Cobordism of maps on $Z_2$-Witt spaces

Algebraic Topology 2014-03-11 v1

Authors: Jean-Paul Brasselet , Alice Kimie Miwa Libardi , Eliris Rizziolli , Marcelo Saia

Abstract

In this article we study the bordism groups of normally nonsingular maps $f: X \to Y$ defined on pseudomanifolds $X$ and $Y$ . To characterize the bordism of such maps, inspired by the formula given by Stong, we give a general definition of Stiefel-Whitney numbers defined on $X$ and $Y$ using the Wu classes defined by Goresky and Pardon and we show that in several cases the cobordism class of a normally nonsingular map $f:X \to Y$ guarantees that these numbers are zero.

Keywords

cobordism normally nonsingular map pseudomanifold Stiefel-Whitney number Wu class

Cite

@article{arxiv.1403.1983,
  title  = {Cobordism of maps on $Z_2$-Witt spaces},
  author = {Jean-Paul Brasselet and Alice Kimie Miwa Libardi and Eliris Rizziolli and Marcelo Saia},
  journal= {arXiv preprint arXiv:1403.1983},
  year   = {2014}
}

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11 pages

Cobordism of maps on $Z_2$-Witt spaces

Abstract

Keywords

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