SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $S^{2}$ but do not admit a spine (that is, a piecewise linear embedding of $S^{2}$ that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2019-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000112/type/journal_article |
| _version_ | 1811156185301123072 |
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| author | ADAM SIMON LEVINE TYE LIDMAN |
| author_facet | ADAM SIMON LEVINE TYE LIDMAN |
| author_sort | ADAM SIMON LEVINE |
| collection | DOAJ |
| description | We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $S^{2}$ but do not admit a spine (that is, a piecewise linear embedding of $S^{2}$ that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer $d$ invariants. |
| first_indexed | 2024-04-10T04:47:17Z |
| format | Article |
| id | doaj.art-8678dacc46864eeab041bcf77c088906 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:17Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-8678dacc46864eeab041bcf77c0889062023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.11SIMPLY CONNECTED, SPINELESS 4-MANIFOLDSADAM SIMON LEVINE0TYE LIDMAN1Department of Mathematics, Duke University, Durham, NC 27708, USA;Department of Mathematics, North Carolina State University, Raleigh, NC 27607, USA;We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $S^{2}$ but do not admit a spine (that is, a piecewise linear embedding of $S^{2}$ that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer $d$ invariants.https://www.cambridge.org/core/product/identifier/S2050509419000112/type/journal_article57M2757Q35 |
| spellingShingle | ADAM SIMON LEVINE TYE LIDMAN SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS Forum of Mathematics, Sigma 57M27 57Q35 |
| title | SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS |
| title_full | SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS |
| title_fullStr | SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS |
| title_full_unstemmed | SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS |
| title_short | SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS |
| title_sort | simply connected spineless 4 manifolds |
| topic | 57M27 57Q35 |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000112/type/journal_article |
| work_keys_str_mv | AT adamsimonlevine simplyconnectedspineless4manifolds AT tyelidman simplyconnectedspineless4manifolds |