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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.
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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | PACIFIC JOURNAL OF MATHEMATICS | ||||
Publisher: | PACIFIC JOURNAL MATHEMATICS | ||||
ISSN: | 0030-8730 | ||||
Official Date: | April 1993 | ||||
Dates: |
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Volume: | 158 | ||||
Number: | 2 | ||||
Number of Pages: | 22 | ||||
Page Range: | pp. 243-264 | ||||
Publication Status: | Published |
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