2000 character limit reached
Mod 2 instanton homology and 4-manifolds with boundary
Published 8 Jul 2023 in math.GT and math.DG | (2307.03950v2)
Abstract: Using instanton homology with coefficients in $Z/2$ we construct a homomorphism $q_2$ from the homology cobordism group in dimension 3 to the integers which is not a rational linear combination of the instanton $h$--invariant and the Heegaard Floer correction term $d$. If an oriented homology $3$--sphere $Y$ bounds a smooth, compact, negative definite $4$--manifold without $2$--torsion in its homology then $q_2(Y)\ge0$, with strict inequality if the intersection form is non-standard.
- The index of elliptic operators: I. Ann. of Math., 87:484–530, 1968.
- Floer’s work on instanton homology, knots and surgery. In H. Hofer, C. H. Taubes, A. Weinstein, and E. Zehnder, editors, The Floer Memorial Volume, pages 195–256. Birkhäuser, 1995.
- An infinite-rank summand of the homology cobordism group. Duke Math. J., 172:2365–2432, 2023.
- S. K. Donaldson. An application of gauge theory to four dimensional topology. J. Diff. Geom., 18:279–315, 1983.
- S. K. Donaldson. The orientation of Yang–Mills moduli spaces and 4444–manifold topology. J. Diff. Geom., 26:397–428, 1987.
- S. K. Donaldson. Floer Homology Groups in Yang–Mills Theory. Cambridge University Press, 2002.
- The Geometry of Four-Manifolds. Oxford University Press, 1990.
- M. Miller Eismeier. Equivariant instanton homology. arXiv:1907.01091.
- R. Fintushel and R. J. Stern. Definite 4–manifolds. J. Diff. Geom., 28:133–141, 1988.
- A. Floer. An instanton invariant for 3–manifolds. Comm. Math. Phys., 118:215–240, 1988.
- K. A. Frøyshov. On Floer homology and 4444–manifolds with boundary, 1995. D.Phil. thesis, University of Oxford.
- K. A. Frøyshov. The Seiberg–Witten equations and four-manifolds with boundary. Math. Res. Lett., 3:373–390, 1996.
- K. A. Frøyshov. Equivariant aspects of Yang–Mills Floer theory. Topology, 41:525–552, 2002.
- K. A. Frøyshov. An inequality for the hℎhitalic_h–invariant in instanton Floer theory. Topology, 43:407–432, 2004.
- K. A. Frøyshov. Compactness and gluing theory for monopoles, volume 15 of Geometry & Topology Monographs. Geometry & Topology Publications, 2008.
- K. A. Frøyshov. Monopole Floer homology for rational homology 3333–spheres. Duke Math. J., 155:519–576, 2010.
- K. A. Frøyshov. 4444–manifolds and intersection forms with local coefficients. J. Diff. Geom., 91:233–259, 2012.
- M. W. Hirsch. Differential Topology. Springer, 1976.
- D. Husemoller and J. Milnor. Symmetric Bilinear Forms. Springer-Verlag, 1973.
- D. Kotschick. SO(3)𝑆𝑂3SO(3)italic_S italic_O ( 3 )–invariants for 4-manifolds with b2+=1superscriptsubscript𝑏21b_{2}^{+}=1italic_b start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT = 1. Proc. London Math. Soc., 63(3):426–448, 1991.
- Embedded surfaces and the structure of Donaldson’s polynomial invariants. J. Diff. Geom., 41:573–734, 1995.
- Monopoles and Three-Manifolds. Cambridge University Press, 2007.
- Knot homology groups from instantons. J. Topology, 4:835–918, 2011.
- Jeffrey M. Lee. Manifolds and Differential Geometry. AMS, 2009.
- Filtered instanton Floer homology and the homology cobordism group. J. Eur. Math. Soc. (2023, online), arXiv:1905.04001.
- H. Ogawa. Lower bounds for solutions of differential inequalities in Hilbert space. Proc. AMS, 16:1241–1243, 1965.
- P. S. Ozsváth and Z. Szabó. Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary. Adv. Math., 173:179–261, 2003.
- P. S. Ozsváth and Z. Szabó. On the Floer homology of plumbed three-manifolds. Geometry & Topology, 7:185–224, 2003.
- Ch. W. Scaduto. On definite lattices bounded by a homology 3333–sphere and Yang-Mills instanton Floer theory. arXiv:1805.07875, to appear in Geometry & Topology.
- Ch. W. Scaduto. Instantons and odd Khovanov homology. J. Topology, 8(3):744––810, 2015.
- E. H. Spanier. Algebraic Topology. McGraw-Hill, 1966. Reprinted by Springer-Verlag.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.