# The Library

### FIXED-POINTS OF BOUNDARY-PRESERVING MAPS OF SURFACES

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UNSPECIFIED.
(1993)
*FIXED-POINTS OF BOUNDARY-PRESERVING MAPS OF SURFACES.*
PACIFIC JOURNAL OF MATHEMATICS, 158
(2).
pp. 243-264.
ISSN 0030-8730

**Full text not available from this repository.**

## Abstract

Let X be a compact 2-manifold with nonempty boundary partial derivative X. Given a boundary-preserving map f: (X, partial derivative X) --> (X, partial derivative X), let MF(partial derivative)[f] denote the minimum number of fixed points of all boundary-preserving maps homotopic to f as maps of pairs and let N(partial derivative)(f) be the relative Nielsen number of f in the sense of Schirmer [S]. Call X boundary-Wecken, bW, if MF(partial derivative)[J] = N(partial derivative)(f) for all boundary-preserving maps of X, almost bW if MF(partial derivative)[f] - N(partial derivative)(f) is bounded for all such f, and totally non-bW otherwise. We show that if the euler characteristic of X is non-negative, then X is bW. On the other hand, except for a relatively small number of cases, we demonstrate that the 2-manifolds of negative euler characteristic are totally non-bW. For one of the remaining cases, the pants surface P, we use techniques of transversality theory to examine the fixed point behavior of boundary-preserving maps of P, and show that P is almost bW.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | PACIFIC JOURNAL OF MATHEMATICS |

Publisher: | PACIFIC JOURNAL MATHEMATICS |

ISSN: | 0030-8730 |

Official Date: | April 1993 |

Volume: | 158 |

Number: | 2 |

Number of Pages: | 22 |

Page Range: | pp. 243-264 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/21474 |

Data sourced from Thomson Reuters' Web of Knowledge

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