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182:'s approach is to group the fixed-point set into classes, which are judged "essential" or "nonessential" according to whether or not they can be "removed" by a homotopy.
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357:'s initial work, the two invariants were combined into a single "generalized Lefschetz number" (more recently called the
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178:. The minimal number was very difficult to compute in Nielsen's time, and remains so today.
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as paths. The equivalence classes with respect to this relation are called the
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making his invariant a good tool for estimating the much more difficult
152:{\displaystyle {\mathit {MF}}=\min\{\#\mathrm {Fix} (g)\,|\,g\sim f\},}
188:'s original formulation is equivalent to the following: We define an
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258:) is defined as the number of Nielsen classes having non-zero
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40:. Its central ideas were developed by Danish mathematician
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Discontinuous groups of isometries in the hyperbolic plane
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is a branch of mathematical research with its origins in
332:. This leads immediately to what is now known as the
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47:The theory developed in the study of the so-called
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341:Because of its definition in terms of the
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192:on the set of fixed points of a self-map
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318:{\displaystyle N(f)\leq {\mathit {MF}},}
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402:Survey article on Nielsen theory
386:(2003). Asmus L. Schmidt (ed.).
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208:if and only if there exists a
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334:Nielsen fixed-point theorem:
18:Nielsen fixed-point theorem
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426:Fixed points (mathematics)
349:is closely related to the
62:space to itself, denoted
353:. Indeed, shortly after
404:by Robert F. Brown at
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170:of mappings, and #Fix(
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66:. This is defined as:
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44:, and bear his name.
421:Fixed-point theorems
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190:equivalence relation
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27:Mathematical branch
359:Reidemeister trace
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38:fixed-point theory
343:fixed-point index
260:fixed-point index
204:is equivalent to
16:(Redirected from
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367:Reidemeister
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196:on a space
35:topological
415:Categories
245:, and the
166:indicates
291:≤
138:∼
105:#
431:Topology
168:homotopy
355:Nielsen
266:Nielsen
186:Nielsen
180:Nielsen
60:compact
58:from a
363:Wecken
345:, the
162:where
361:) by
262:sum.
223:with
215:from
51:of a
365:and
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219:to
99:min
53:map
417::
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64:MF
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