A splitting theorem for the Seiberg-Witten invariant of a homology \(S^1\times S^3\)

DOI10.2140/gt.2018.22.2865zbMath1427.57014arXiv1702.04417OpenAlexW2589106366MaRDI QIDQ1637315

Nikolai Saveliev, Daniel Ruberman, Jianfeng Lin

Publication date: 8 June 2018

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04417

zbMATH Keywords

Seiberg-Witten invarianthomology cobordismmonopole Floer homologyFrøyshov invariantmanifolds with \(\mathbb Z/2\) homology \(S^1\times S^3\)manifolds with homology \(S^1\times S^3\)

Mathematics Subject Classification ID

Applications of global analysis to structures on manifolds (57R57) Exotic index theories on manifolds (58J22) Floer homology (57R58) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Eta-invariants, Chern-Simons invariants (58J28) Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) (57K41)

Related Items (10)

Seifert hypersurfaces of 2-knots and Chern-Simons functional ⋮ Rank inequalities for the Heegaard Floer homology of branched covers ⋮ On homology cobordism and local equivalence between plumbed manifolds ⋮ Ribbon homology cobordisms ⋮ Positive scalar curvature and homology cobordism invariants ⋮ On the Frøyshov invariant and monopole Lefschetz number ⋮ On the spectral sets of Inoue surfaces ⋮ Positive scalar curvature and 10/8-type inequalities on 4-manifolds with periodic ends ⋮ APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY ⋮ On the monopole Lefschetz number of finite-order diffeomorphisms

Cites Work

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• Surgery obstructions and Heegaard Floer homology
• Cosmetic surgeries on knots in \(S^3\)
• On the Heegaard Floer homology of branched double-covers
• Monopole Floer homology for rational homology 3-spheres
• Knot Floer homology and rational surgeries
• Embedded contact homology and Seiberg-Witten Floer cohomology. I.
• A link surgery spectral sequence in monopole Floer homology
• The \({\bar\mu}\)-invariant of Seifert fibered homology spheres and the Dirac operator
• Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant
• Differentiable structures on punctured 4-manifolds
• A gluing theorem for the relative Bauer-Furuta invariants
• Surgery and harmonic spinors
• On the structure of manifolds with positive scalar curvature
• Generic metrics and connections on spin- and \(\text{spin}^c\)-manifolds
• Seiberg-Witten monopoles on Seifert fibered spaces
• Heegaard Floer homology and alternating knots
• A connected sum formula for involutive Heegaard Floer homology
• Holomorphic disks and three-manifold invariants: properties and applications
• Fukumoto-Furuta invariants of plumbed homology 3-spheres.
• Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
• Holomorphic disks and knot invariants
• Rohlin's invariant and gauge theory. II: Mapping tori
• Monopoles and four-manifolds
• The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology
• A categorification of the Jones polynomial
• An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields
• Involutive Heegaard Floer homology
• On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds
• Knot Floer homology and integer surgeries
• Monopoles and lens space surgeries
• An index theorem for end-periodic operators
• Pin(2)-Equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
• Spectral asymmetry and Riemannian Geometry. I
• Manolescu invariants of connected sums
• Patterns in Knot Cohomology, I
• \(W\)-invariants and Neumann-Siebenmann invariants for Seifert homology 3-spheres

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