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In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations necessary to build the spectral sequence and give a convenient description of its E2-page. Our description of the E2-page is in terms of homology of the local system of fibers, which is given using a theory similar to Rost’s cycle modules. We close by providing some sample applications of the spectral sequence and some hints at future work.
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Instantons and Bar-Natan homology
A spectral sequence is established whose $$E_{2}$$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $$E_{2}$$ page is a characteristic-2 version of $$F_{5}$$ homology in Khovanov's classification.
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- PAR ID:
- 10105143
- Date Published:
- Journal Name:
- Compositio Mathematica
- Volume:
- 157
- Issue:
- 3
- ISSN:
- 0010-437X
- Page Range / eLocation ID:
- 484 to 528
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1112/s0010437x2000768x
