Journal article
On the algebra of cornered Floer homology
- Abstract:
- Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2‐algebra, the nil‐Coxeter sequential 2‐algebra and to a surface with connected boundary an algebra‐module over this 2‐algebra, such that a natural gluing property is satisfied. Moreover, with a view towards the structure of a potential Floer homology theory of 3‐manifolds with codimension‐2 corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 778.6KB, Terms of use)
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- Publisher copy:
- 10.1112/jtopol/jtt013
Authors
- Publisher:
- London Mathematical Society
- Journal:
- Journal of Topology More from this journal
- Volume:
- 7
- Issue:
- 1
- Pages:
- 1-68
- Publication date:
- 2013-06-12
- DOI:
- EISSN:
-
1753-8424
- ISSN:
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1753-8416
Terms of use
- Copyright holder:
- London Mathematical Society
- Copyright date:
- 2013
- Notes:
- © 2013 London Mathematical Society. This is the accepted manuscript version of the article. The final version is available online from London Mathematical Society at: https://doi.org/10.1112/jtopol/jtt013
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