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Minimizing the number of Nielsen preimage classes
Olga Frolkina
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Geometry & Topology Monographs 14
(2008) 193–217
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Abstract
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We find conditions on topological spaces X, Y and nonempty subset
B of Y which guarantee that for each continuous map
f:X→ Y there exists a map g∼ f such that
Nielsen preimage classes of g-1(B) are all topologically
essential.
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I feel very honoured to have the
possibility to contribute a paper to this volume dedicated to
the memory of an outstanding mathematician and a pleasant
good-humoured person: Heiner Zieschang.
In 2002–2003 in M V Lomonosov Moscow State
University Heiner gave a series of lectures on fixed points
and coincidence theory, which I was lucky to attend. In the
same period I learned the German language at his seminars.
During a nice voyage in summer 2003 from Moscow to Saint
Petersburg, in which I was invited to take part, I made the
acquaintance with his wife Ute and daughter Kim; two years
later I met his other daughter Tanja. Heiner guided my study
of coincidences, intersections and preimages during my visit
in November–December 2004 in Ruhr-Universität
Bochum. It was planned, to continue the project in 2005.
But that hope was doomed to disappointment….
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Keywords
preimage problem, Nielsen preimage class,
topological essentiality, Nielsen preimage number, minimum
number of preimage classes
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Mathematical Subject Classification
Primary: 54H99, 55M99
Secondary: 55S35
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Publication
Received: 30 March 2006
Revised: 4 March 2007
Accepted: 18 April 2007
Published: 29 April 2008
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