FIXED-POINTS OF BOUNDARY-PRESERVING MAPS OF SURFACES
UNSPECIFIED. (1993) FIXED-POINTS OF BOUNDARY-PRESERVING MAPS OF SURFACES. PACIFIC JOURNAL OF MATHEMATICS, 158 (2). pp. 243-264. ISSN 0030-8730Full text not available from this repository.
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|
|Official Date:||April 1993|
|Number of Pages:||22|
|Page Range:||pp. 243-264|
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