The Michigan Mathematical Journal

A Remark on Pin(2)-Equivariant Floer Homology

Matthew Stoffregen

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Abstract

In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms d̲,d¯, are related to the Pin(2)-equivariant Floer homology SWFH∗G. We show that the only interesting correction terms of a Pin(2)-space are those coming from the subgroups Z/4, S1, and Pin(2) itself.

Article information

Source
Michigan Math. J., Volume 66, Issue 4 (2017), 867-884.

Dates
Received: 14 July 2016
Revised: 12 October 2016
First available in Project Euclid: 24 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1508810818

Digital Object Identifier
doi:10.1307/mmj/1508810818

Mathematical Reviews number (MathSciNet)
MR3720328

Zentralblatt MATH identifier
06822190

Subjects
Primary: 57R58: Floer homology 57M27: Invariants of knots and 3-manifolds

Citation

Stoffregen, Matthew. A Remark on $\operatorname{Pin}(2)$ -Equivariant Floer Homology. Michigan Math. J. 66 (2017), no. 4, 867--884. doi:10.1307/mmj/1508810818. https://projecteuclid.org/euclid.mmj/1508810818


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References

  • [1] V. Colin, P. Ghiggini, and K. Honda,${HF}={ECH}$ via open book decompositions: A summary, 2011,http://arxiv.org/abs/1103.1290.
  • [2] K. A. Frøyshov,Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002), no. 3, 525–552.
  • [3] D. E. Galewski and R. J. Stern,Classification of simplicial triangulations of topological manifolds, Ann. of Math. (2) 111 (1980), no. 1, 1–34.
    Mathematical Reviews (MathSciNet): MR558395
    Zentralblatt MATH: 0441.57017
    Digital Object Identifier: doi:10.2307/1971215
  • [4] A. Hatcher,Algebraic topology, Cambridge University Press, Cambridge, 2002.
    Zentralblatt MATH: 1044.55001
  • [5] K. Hendricks and C. Manolescu,Involutive Heegaard–Floer homology, 2015,http://arxiv.org/pdf/1507.00383.
    Mathematical Reviews (MathSciNet): MR3649355
    Digital Object Identifier: doi:10.1215/00127094-3793141
    Project Euclid: euclid.dmj/1484103841
  • [6] P. Kronheimer and T. Mrowka,Monopoles and three-manifolds, New Math. Monogr., 10, Cambridge University Press, Cambridge, 2007.
    Zentralblatt MATH: 1158.57002
  • [7] C. Kutluhan, Y.-J. Lee, and C. H. Taubes,HF = HM I: Heegaard Floer homology and Seiberg–Witten Floer homology, 2010,http://arxiv.org/abs/1007.1979.
  • [8] F. Lin,A Morse–Bott approach to monopole Floer homology and the Triangulation conjecture, 2014,http://arxiv.org/abs/1404.4561.
  • [9] F. Lin,The surgery exact triangle in $\operatorname{Pin}(2)$-monopole Floer homology, 2015,http://arxiv.org/abs/1504.01993.
  • [10] C. Manolescu,On the intersection forms of spin four-manifolds with boundary, Math. Ann. 359 (2014), no. 3–4, 695–728.
    Zentralblatt MATH: 1305.57050
    Digital Object Identifier: doi:10.1007/s00208-014-1010-1
  • [11] C. Manolescu,$\operatorname{Pin}(2)$-equivariant Seiberg–Witten Floer homology and the triangulation conjecture, J. Amer. Math. Soc. 29 (2017), 147–167.
  • [12] T. Matumoto,Triangulation of manifolds, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, CA, 1976), part 2, Proc. Sympos. Pure Math., XXXII, pp. 3–6, Amer. Math. Soc., Providence, RI, 1978.
  • [13] P. Ozsváth and Z. Szabó,Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (2004), no. 3, 1159–1245.
    Zentralblatt MATH: 1081.57013
    Digital Object Identifier: doi:10.4007/annals.2004.159.1159
  • [14] P. Ozsváth and Z. Szabó,Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158.
  • [15] M. Stoffregen,Manolescu invariants of connected sums, 2015,http://arxiv.org/abs/1510.01286.
    Zentralblatt MATH: 06818140
    Digital Object Identifier: doi:10.1112/plms.12060
  • [16] M. Stoffregen,$\operatorname{Pin}(2)$-equivariant Seiberg–Witten Floer homology of Seifert fiberations, 2015,http://arxiv.org/abs/1505.03234.
  • [17] T. tom Dieck,Transformation groups, De Gruyter Stud. Math., 8, de Gruyter, Berlin, 1987.

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