| Title:
|
Higher simple structure sets of lens spaces with the fundamental group of arbitrary order (English) |
| Author:
|
Balko, L’udovít |
| Author:
|
Macko, Tibor |
| Author:
|
Niepel, Martin |
| Author:
|
Rusin, Tomáš |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2019 |
| Pages:
|
267-280 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to $3$. (English) |
| Keyword:
|
fake lens space |
| Keyword:
|
higher structure set |
| Keyword:
|
$\rho $-invariant |
| Keyword:
|
surgery |
| MSC:
|
57R65 |
| MSC:
|
57S25 |
| idZBL:
|
Zbl 07144742 |
| idMR:
|
MR4057924 |
| DOI:
|
10.5817/AM2019-5-267 |
| . |
| Date available:
|
2019-12-09T12:20:08Z |
| Last updated:
|
2020-11-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147940 |
| . |
| Reference:
|
[1] Balko, L’., Macko, T., Niepel, M., Rusin, T.: Higher simple structure sets of lens spaces with the fundamental group of order $2^K$..Topology Appl. 263 (2019), 299–320 (English). MR 3969225 |
| Reference:
|
[2] Hambleton, I., Taylor, L.R.: A guide to the calculation of the surgery obstruction groups for finite groups.Surveys on surgery theory, Vol. 1, Ann. of Math. Stud., vol. 145, Princeton Univ. Press, Princeton, NJ, 2000, pp. 225–274. MR MR1747537 (2001e:19007) MR 1747537 |
| Reference:
|
[3] López de Medrano, S.: Involutions on manifolds.Springer-Verlag, New York, 1971, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 59. MR MR0298698 (45 #7747) MR 0298698 |
| Reference:
|
[4] Macko, T., Wegner, Ch.: On fake lens spaces with fundamental group of order a power of 2.Algebr. Geom. Topol. 9 (2009), no. 3, 1837–1883. MR 2550097 (2010k:57067) DOI: http://dx.doi.org/10.2140/agt.2009.9.1837 MR 2550097, 10.2140/agt.2009.9.1837 |
| Reference:
|
[5] Macko, T., Wegner, Ch.: On the classification of fake lens spaces.Forum Math. 23 (2011), no. 5, 1053–1091. MR 2836378 DOI: http://dx.doi.org/10.1515/FORM.2011.038 MR 2836378, 10.1515/form.2011.038 |
| Reference:
|
[6] Madsen, I., Milgram, R.J.: The classifying spaces for surgery and cobordism of manifolds.Annals of Mathematics Studies, vol. 92, Princeton University Press, Princeton, N.J., 1979. MR MR548575 (81b:57014) MR 0548575 |
| Reference:
|
[7] Madsen, I., Rothenberg, M.: On the classification of ${G}$-spheres. II. PL automorphism groups.Math. Scand. 64 (1989), no. 2, 161–218. MR 91d:57024 MR 1037458, 10.7146/math.scand.a-12253 |
| Reference:
|
[8] Quinn, F.: A geometric formulation of surgery.Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969), Markham, Chicago, Ill., 1970, pp. 500–511. MR 43 #8087 MR 0282375 |
| Reference:
|
[9] Wall, C.T.C.: Surgery on compact manifolds.second ed., Mathematical Surveys and Monographs, vol. 69, American Mathematical Society, Providence, RI, 1999, Edited and with a foreword by A. A. Ranicki. MR MR1687388 (2000a:57089) MR 1687388 |
| . |
