Duke Mathematical Journal

Monopole Floer homology for rational homology 3-spheres

Kim A. Frøyshov

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We give a new construction of monopole Floer homology for spinc rational homology 3-spheres. As applications, we define two invariants of certain 4-manifolds with b1=1 and b+=0.

Article information

Duke Math. J., Volume 155, Number 3 (2010), 519-576.

First available in Project Euclid: 16 November 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R58: Floer homology
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]


Frøyshov, Kim A. Monopole Floer homology for rational homology 3-spheres. Duke Math. J. 155 (2010), no. 3, 519--576. doi:10.1215/00127094-2010-060. https://projecteuclid.org/euclid.dmj/1289916772

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  • D. M. Austin and P. J. Braam, ``Morse-Bott theory and equivariant cohomology'' in The Floer Memorial Volume, Progr. Math. 133, Birkhäuser, Basel, 1995, 123--183.
  • A. Banyaga and D. Hurtubise, Lectures on Morse Homology, Kluwer Texts Math. Sci. 29, Kluwer Acad. Publ., Dordrecht, 2004.
  • Ch. Bär, Harmonic spinors for twisted Dirac operators, Math. Ann. 309 (1997), 225--246.
  • S. K. Donaldson, Floer Homology Groups in Yang-Mills Theory, Cambridge Tracts in Math. 147, Cambridge Univ. Press, Cambridge, 2002.
  • N. D. Elkies, A characterization of the $\z^n$ lattice, Math. Res. Lett. 2 (1995), 321--326.
  • A. Floer, An instanton-invariant for 3-manifolds, Comm. Math. Phys. 118 (1988), 215--240.
  • K. A. Frøyshov, The Seiberg-Witten equations and four-manifolds with boundary, Math. Res. Lett. 3 (1996), 373--390.
  • —, Equivariant aspects of Yang-Mills Floer theory, Topology 41 (2002), 525--552.
  • —, Compactness and Gluing Theory for Monopoles, Geom. Topol. Monogr. 15, Geom. Topol. Publ., Coventry, 2008.
  • M. Furuta and H. Ohta, Differentiable structures on punctured $4$-manifolds, Topology Appl. 51 (1993), 291--301.
  • N. Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1--55.
  • J. Kazdan, Unique continuation in geometry, Comm. Pure Appl. Math. 41 (1988), 667--681.
  • P. Kronheimer and T. Mrowka, Monopoles and Three-Manifolds, New Math. Monogr. 10, Cambridge Univ. Press, Cambridge, 2007.
  • Y. Lim, The equivalence of Seiberg-Witten and Casson invariants for homology $3$-spheres, Math. Res. Lett. 6 (1999), 631--643.
  • M. Marcolli and B.-L. Wang, Equivariant Seiberg-Witten Floer homology, Comm. Anal. Geom. 9 (2001), 451--639.
  • Ch. Okonek and A. Teleman, ``Seiberg-Witten invariants for $4$-manifolds with $b_+=0$'' in Complex Analysis and Algebraic Geometry, Walter de Gruyter, Berlin, 2000, 347--357.
  • P. Ozsváth and Z. Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003), 179--261.
  • —, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), 1027--1158.
  • J. Robbin and D. Salamon, The spectral flow and the Maslov index, Bull. Lond. Math. Soc. 27 (1995), 1--33.
  • D. Ruberman and N. Saveliev, Rohlin's invariant and gauge theory, II: Mapping tori, Geom. Topol. 8 (2004), 35--76.
  • A. Teleman, Donaldson theory on non-Kählerian surfaces and class VII surfaces with $b_2=1$, Invent. Math. 162 (2005), 493--521.