Smoothings of piecewise linear manifolds:
The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
1974
|
| Series: | Annals of Mathematics Studies
number 80 |
| Subjects: | |
| Online Access: | Volltext |
| Summary: | The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Physical Description: | 1 online resource |
| ISBN: | 9781400881680 |
| DOI: | 10.1515/9781400881680 |
Staff View
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| 245 | 1 | 0 | |a Smoothings of piecewise linear manifolds |c Barry Mazur, Morris W. Hirsch |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 1974 | |
| 264 | 4 | |c © 1974 | |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 80 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure | ||
| 546 | |a In English | ||
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Record in the Search Index
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| author | Hirsch, Morris W. 1933- Mazur, Barry 1937- |
| author_GND | (DE-588)172139120 (DE-588)107715945 |
| author_facet | Hirsch, Morris W. 1933- Mazur, Barry 1937- |
| author_role | aut aut |
| author_sort | Hirsch, Morris W. 1933- |
| author_variant | m w h mw mwh b m bm |
| building | Verbundindex |
| bvnumber | BV043712428 |
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| ctrlnum | (ZDB-23-DGG)9781400881680 (OCoLC)1165548197 (DE-599)BVBBV043712428 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400881680 |
| format | Electronic eBook |
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| id | DE-604.BV043712428 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400881680 |
| language | English |
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| series | Annals of Mathematics Studies |
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| spelling | Hirsch, Morris W. 1933- (DE-588)172139120 aut Smoothings of piecewise linear manifolds Barry Mazur, Morris W. Hirsch Princeton, NJ Princeton University Press 1974 © 1974 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 80 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure In English Manifolds (Mathematics) Piecewise linear topology Glättung (DE-588)4157404-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Glättung (DE-588)4157404-7 s 1\p DE-604 Mazur, Barry 1937- (DE-588)107715945 aut Erscheint auch als Druck-Ausgabe 0-691-08145-X Annals of Mathematics Studies number 80 (DE-604)BV040389493 80 https://doi.org/10.1515/9781400881680?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hirsch, Morris W. 1933- Mazur, Barry 1937- Smoothings of piecewise linear manifolds Annals of Mathematics Studies Manifolds (Mathematics) Piecewise linear topology Glättung (DE-588)4157404-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4157404-7 (DE-588)4037379-4 |
| title | Smoothings of piecewise linear manifolds |
| title_auth | Smoothings of piecewise linear manifolds |
| title_exact_search | Smoothings of piecewise linear manifolds |
| title_full | Smoothings of piecewise linear manifolds Barry Mazur, Morris W. Hirsch |
| title_fullStr | Smoothings of piecewise linear manifolds Barry Mazur, Morris W. Hirsch |
| title_full_unstemmed | Smoothings of piecewise linear manifolds Barry Mazur, Morris W. Hirsch |
| title_short | Smoothings of piecewise linear manifolds |
| title_sort | smoothings of piecewise linear manifolds |
| topic | Manifolds (Mathematics) Piecewise linear topology Glättung (DE-588)4157404-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Manifolds (Mathematics) Piecewise linear topology Glättung Mannigfaltigkeit |
| url | https://doi.org/10.1515/9781400881680?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT hirschmorrisw smoothingsofpiecewiselinearmanifolds AT mazurbarry smoothingsofpiecewiselinearmanifolds |