Heegaard Floer invariants in codimension one
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- by Adam Simon Levine and Daniel Ruberman PDF
- Trans. Amer. Math. Soc. 371 (2019), 3049-3081 Request permission
Abstract:
Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a generator of $H_3(X)$, a suitable version of the Heegaard Floer $d$ invariant of $Y$, defined using twisted coefficients, is a diffeomorphism invariant of $X$. We show how this invariant can be used to obstruct embeddings of certain types of $3$-manifolds, including those obtained as a connected sum of a rational homology $3$-sphere and any number of copies of $S^1 \times S^2$. We also give similar obstructions to embeddings in certain open $4$-manifolds, including exotic $\mathbb {R}^4$s.References
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Additional Information
- Adam Simon Levine
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08540
- Address at time of publication: Department of Mathematics, Duke University, Durham, North Carolina 27708
- MR Author ID: 849574
- ORCID: 0000-0002-9084-5124
- Email: alevine@math.duke.edu
- Daniel Ruberman
- Affiliation: Department of Mathematics, MS 050, Brandeis University, Waltham, Massachusetts 02454
- Email: ruberman@brandeis.edu
- Received by editor(s): October 23, 2016
- Received by editor(s) in revised form: July 17, 2017
- Published electronically: October 1, 2018
- Additional Notes: The first author was partially supported by NSF grant DMS-1405378.
The second author was partially supported by NSF grant DMS-1506328. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 3049-3081
- MSC (2010): Primary 57R58
- DOI: https://doi.org/10.1090/tran/7345
- MathSciNet review: 3896105