The Michigan Mathematical Journal

Relative Q-Gradings from Bordered Floer Theory

Robert Lipshitz, Peter Ozsváth, and Dylan P. Thurston

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Abstract

In this paper, we show how to recover the relative Q-grading in Heegaard Floer homology from the noncommutative grading on bordered Floer homology.

Article information

Source
Michigan Math. J., Volume 67, Issue 4 (2018), 827-838.

Dates
Received: 7 February 2017
Revised: 26 March 2017
First available in Project Euclid: 17 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1539763499

Digital Object Identifier
doi:10.1307/mmj/1539763499

Mathematical Reviews number (MathSciNet)
MR3877439

Zentralblatt MATH identifier
07056371

Subjects
Primary: 57R58: Floer homology
Secondary: 57M27: Invariants of knots and 3-manifolds 53D40: Floer homology and cohomology, symplectic aspects

Citation

Lipshitz, Robert; Ozsváth, Peter; Thurston, Dylan P. Relative $\mathbb{Q}$ -Gradings from Bordered Floer Theory. Michigan Math. J. 67 (2018), no. 4, 827--838. doi:10.1307/mmj/1539763499. https://projecteuclid.org/euclid.mmj/1539763499


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References

  • [1] J. E. Greene, Lattices, graphs, and Conway mutation, Invent. Math. 192 (2013), no. 3, 717–750.
  • [2] K. A. Frøyshov, An inequality for the $h$-invariant in instanton Floer theory, Topology 43 (2004), no. 2, 407–432.
  • [3] Y. Huang and V. G. B. Ramos, A topological grading on bordered Heegaard Floer homology, Quantum Topol. 6 (2015), no. 3, 403–449.
  • [4] Y. Huang and V. G. B. Ramos, An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields, 2011, arXiv:1112.0290.
  • [5] P. Kronheimer and T. Mrowka, Monopoles and three-manifolds, New Math. Monogr., 10, Cambridge University Press, Cambridge, 2007.
  • [6] D. A. Lee and R. Lipshitz, Covering spaces and $\mathbb{Q}$-gradings on Heegaard Floer homology, J. Symplectic Geom. 6 (2008), no. 1, 33–59.
  • [7] R. Lipshitz, A cylindrical reformulation of Heegaard Floer homology, Geom. Topol. 10 (2006), 955–1097.
  • [8] R. Lipshitz, P. Ozsváth, and D. Thurston, Bimodules in bordered Heegaard Floer homology, Geom. Topol. 19 (2015), no. 2, 525–724.
  • [9] R. Lipshitz, P. S. Ozsváth, and D. P. Thurston, Computing $\widehat{\mathit{HF}}$ by factoring mapping classes, Geom. Topol. 18 (2014), no. 5, 2547–2681.
  • [10] R. Lipshitz, P. S. Ozsváth, and D. P. Thurston, Bordered Heegaard Floer homology: invariance and pairing, 2008, arXiv:0810.0687.
  • [11] P. S. Ozsváth and Z. Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003), 179–261.
  • [12] P. S. Ozsváth and Z. Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158.
  • [13] P. S. Ozsváth and Z. Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005), no. 6, 1281–1300.
  • [14] P. S. Ozsváth and Z. Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006), no. 2, 326–400.
  • [15] R. Rustamov, Surgery formula for the renormalized Euler characteristic of Heegaard Floer homology, 2004, arXiv:math/0409294.
  • [16] S. Sarkar, Maslov index formulas for Whitney $n$-gons, J. Symplectic Geom. 9 (2011), no. 2, 251–270.
  • [17] S. Sarkar and J. Wang, An algorithm for computing some Heegaard Floer homologies, Ann. of Math. (2) 171 (2010), no. 2, 1213–1236.