2017
Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres
VOKŘÍNEK, LukášBasic information
Original name
Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres
Authors
VOKŘÍNEK, Lukáš (203 Czech Republic, guarantor, belonging to the institution)
Edition
Discrete & Computational Geometry, New York, Springer, 2017, 0179-5376
Other information
Language
English
Type of outcome
Article in a journal
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
is not subject to a state or trade secret
Impact factor
Impact factor: 0.672
RIV identification code
RIV/00216224:14310/17:00094700
Organization unit
Faculty of Science
UT WoS
000393700500001
EID Scopus
2-s2.0-84995807116
Keywords in English
Homotopy class; Computation; Higher difference
Tags
International impact, Reviewed
Changed: 31/3/2018 11:13, Ing. Nicole Zrilić
Abstract
In the original language
In a recent paper (Cadek et al., Discrete Comput Geom 51: 24- 66, 2014), it was shown that the problem of the existence of a continuous map X -> Y extending a given map A -> Y, defined on a subspace A subset of X , is undecidable, even for Y an even-dimensional sphere. In the present paper, we prove that the same problem for Y an odd-dimensional sphere is decidable. More generally, the same holds for any d-connected target space Y whose homotopy groups pi_n(Y) are finite for 2d < n < dim X. We also prove an equivariant version, where all spaces are equipped with free actions of a given finite group G and all maps are supposed to respect these actions. This yields the computability of the Z/2-index of a given space up to an uncertainty of 1.
Links
| GBP201/12/G028, research and development project |
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