A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory ( $SHM$ ). Our invariant can be viewed as a generalization of Kronhe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2016-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509416000116/type/journal_article |
| _version_ | 1811156241388404736 |
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| author | JOHN A. BALDWIN STEVEN SIVEK |
| author_facet | JOHN A. BALDWIN STEVEN SIVEK |
| author_sort | JOHN A. BALDWIN |
| collection | DOAJ |
| description | We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory (
$SHM$
). Our invariant can be viewed as a generalization of Kronheimer and Mrowka’s contact invariant for closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, and Matić’s contact invariant in sutured Heegaard Floer homology (
$SFH$
). In the process of defining our invariant, we construct maps on
$SHM$
associated to contact handle attachments, analogous to those defined by Honda, Kazez, and Matić in
$SFH$
. We use these maps to establish a bypass exact triangle in
$SHM$
analogous to Honda’s in
$SFH$
. This paper also provides the topological basis for the construction of similar gluing maps in sutured instanton Floer homology, which are used in Baldwin and Sivek [Selecta Math. (N.S.), 22(2) (2016), 939–978] to define a contact invariant in the instanton Floer setting. |
| first_indexed | 2024-04-10T04:47:15Z |
| format | Article |
| id | doaj.art-79d67f478fc749c5be2610be9d8ac157 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:15Z |
| publishDate | 2016-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-79d67f478fc749c5be2610be9d8ac1572023-03-09T12:34:41ZengCambridge University PressForum of Mathematics, Sigma2050-50942016-01-01410.1017/fms.2016.11A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGYJOHN A. BALDWIN0STEVEN SIVEK1Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, USA;Department of Mathematics, Princeton University, Princeton, NJ 08544-1000, USA;We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory ( $SHM$ ). Our invariant can be viewed as a generalization of Kronheimer and Mrowka’s contact invariant for closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, and Matić’s contact invariant in sutured Heegaard Floer homology ( $SFH$ ). In the process of defining our invariant, we construct maps on $SHM$ associated to contact handle attachments, analogous to those defined by Honda, Kazez, and Matić in $SFH$ . We use these maps to establish a bypass exact triangle in $SHM$ analogous to Honda’s in $SFH$ . This paper also provides the topological basis for the construction of similar gluing maps in sutured instanton Floer homology, which are used in Baldwin and Sivek [Selecta Math. (N.S.), 22(2) (2016), 939–978] to define a contact invariant in the instanton Floer setting.https://www.cambridge.org/core/product/identifier/S2050509416000116/type/journal_article53D10 (primary)53D4057R58 (secondary) |
| spellingShingle | JOHN A. BALDWIN STEVEN SIVEK A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY Forum of Mathematics, Sigma 53D10 (primary) 53D40 57R58 (secondary) |
| title | A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY |
| title_full | A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY |
| title_fullStr | A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY |
| title_full_unstemmed | A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY |
| title_short | A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY |
| title_sort | contact invariant in sutured monopole homology |
| topic | 53D10 (primary) 53D40 57R58 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050509416000116/type/journal_article |
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