an:05360595
Zbl 1153.54018
Ageev, S. M.
Axiomatic method of partitions in the theory of N??beling spaces. II. Unknotting theorem
EN
Sb. Math. 198, No. 5, 597-625 (2007); translation from Mat. Sb. 198, No. 5, 3-32 (2007).
00211191
2007
j
54F65 54C55 54F45 55P15
axiom system of N??beling spaces; unknotting; shrinking of perfect resolution
This is the second part of a series of three papers in which the author proves the following classical conjecture on a characterization of N??beling spaces.
Theorem. For every \(2 \leq k < \infty\), if a strongly \(k\)-universal \(k\) dimensional Polish space is an absolute extensor in dimension \(k\), then it is homeomorphic to the \(k\) dimensional N??beling space \(N_{k}^{2k+1}\).
For the definitions, we refer to the review of the first part, see \textit{S. M. Ageev} [Sb. Math. 198, No.~3, 299--342 (2007; Zbl 1147.54019)].
In the first part of the series of three papers, the author introduced the axiom system of N??beling spaces and discussed several surgery techniques which allow to improve the connectivity properties of partitions. In the present second part the author proves several technical results related to partitions and approximations of maps, and reduces the theorem above to the proof of the consistency of the axiom system of N??beling spaces. The third part contains the final step, i.e. that the so-called N??beling cores of constructible manifolds satisfy the axiom system of N??beling spaces.
Tam??s M??trai (Toronto)
Zbl 1147.54019