Self-adjoint elliptic operators and manifold decompositions Part III: Determinant line bundles and Lagrangian intersection

Cappell, Sylvain E.; Lee, Ronnie; Miller, Edward Y.

doi:10.1002/(sici)1097-0312(199905)52:5<543::aid-cpa1>3.0.co;2-o

Cited by 10 publications

(5 citation statements)

References 25 publications

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“…To better understand the relationship between λ SU(3) and τ, it is helpful to compare them to the SU (2) invariants λ W and λ BN of rational homology spheres defined by Kevin Walker [10] and by Boyer and Nicas [5], respectively. Under suitable hypotheses, the difference λ W − λ BN can be expressed as a sum of Atiyah-Patodi-Singer rho invariants of U (1) representations [6]. A similar statement is true of λ SU(3) − τ , and so it is natural to ask whether τ is the SU (3) analog of the Boyer-Nicas invariant.…”

Section: Proofsmentioning

confidence: 99%

An integer valued SU(3) Casson invariant

Bodén

Herald

Kirk

2001

Mathematical Research Letters

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Section: Proofsmentioning

confidence: 99%

An integer valued SU(3) Casson invariant

Bodén

Herald

Kirk

2001

Mathematical Research Letters

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“…The proof proceeds by pushing equivariant flat connections from Σ to the homology lens space Σ ′ and identifying the count of the latter connections with a sum of invariants of the type discussed by Boyer-Nicas [7] and Boyer-Lines [6]. Note that these invariants are different from Walker's invariant [51] in that they only count irreducible flat connections over Σ ′ ; their gauge theoretic definition is implicit in work of Cappell, Lee and Miller [9]. An application of surgery formulas and Herald's theorem on equivariant knot signatures [24] completes the proof.…”

Section: Furuta-ohta Vs Equivariant Cassonmentioning

confidence: 99%

Casson-type invariants in dimension four

Ruberman¹,

Saveliev²

2005

Geometry and Topology of Manifolds

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“…Such a subgroup is generated by π -rotations about two perpendicular axes in R 3 , and any two such subgroups are conjugate to each other in SO (3). Hence the following definition makes sense.…”

Section: The Four-orbits and Invariantλmentioning

confidence: 99%

Rohlin’s invariant and gauge theory III. Homology 4–tori

Ruberman

Saveliev

2005

Geom. Topol.

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This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in dimension three, starting with Casson's integral lift of the Rohlin invariant of a homology sphere. We consider two invariants of a spin 4-manifold that has the integral homology of a 4-torus. The first is a degree zero Donaldson invariant, counting flat connections on a certain SO(3)-bundle. The second, which depends on the choice of a 1-dimensional cohomology class, is a combination of Rohlin invariants of a 3-manifold carrying the dual homology class. We prove that these invariants, suitably normalized, agree modulo 2, by showing that they coincide with the quadruple cup product of 1-dimensional cohomology classes.

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Self-adjoint elliptic operators and manifold decompositions Part III: Determinant line bundles and Lagrangian intersection

Cited by 10 publications

References 25 publications

An integer valued SU(3) Casson invariant

An integer valued SU(3) Casson invariant

Casson-type invariants in dimension four

Rohlin’s invariant and gauge theory III. Homology 4–tori

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