Self-adjoint elliptic operators and manifold decompositions part I: Low Eigenmodes and stretching

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

doi:10.1002/(sici)1097-0312(199608)49:8<825::aid-cpa3>3.0.co;2-a

Cited by 39 publications

(72 citation statements)

References 16 publications

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“…We refer to [5] for the following lemma (cf. Lemma 3.1 in [5]). Let φ and ψ be smooth sections on M j (j = 1, 2).…”

Section: Applying Lemma 41 Withmentioning

confidence: 99%

Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

Lee

2003

Trans. Amer. Math. Soc.

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Abstract. The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under an assumption that the product structure is given near the boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.

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“…We refer to [5] for the following lemma (cf. Lemma 3.1 in [5]). Let φ and ψ be smooth sections on M j (j = 1, 2).…”

Section: Applying Lemma 41 Withmentioning

confidence: 99%

Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

Lee

2003

Trans. Amer. Math. Soc.

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“…This follows ( [5]) from the exponential decay (cf [2]) of harmonic forms onN . To take advantage of this, consider a path h t ⊂ Π r (Z) such that ω(g t ) crosses the wall W transversally at t = 0.…”

Section: Theorem 41 the Invariant Sw Tot (F γ Z ) Is Defined And Eqmentioning

confidence: 99%

Positive scalar curvature, diffeomorphisms and the Seiberg–Witten invariants

Ruberman

2001

Geom. Topol.

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We study the space of positive scalar curvature (psc) metrics on a 4-manifold, and give examples of simply connected manifolds for which it is disconnected. These examples imply that concordance of psc metrics does not imply isotopy of such metrics. This is demonstrated using a modification of the 1-parameter Seiberg-Witten invariants which we introduced in earlier work. The invariant shows that the diffeomorphism group of the underlying 4-manifold is disconnected. We also study the moduli space of positive scalar curvature metrics modulo diffeomorphism, and give examples to show that this space can be disconnected. The (non-orientable) 4-manifolds in this case are explicitly described, and the components in the moduli space are distinguished by a P in c eta invariant.

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“…Some of the results here -in particular the counting argument below (23) -appeared previously in the paper [4] of Cappell, Lee and Miller.…”

Section: A Hodge Mayer-vietoris Sequencementioning

confidence: 67%

Analytic surgery and analytic torsion

Hassell¹

1998

Communications in Analysis and Geometry

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Abstract. Analytic surgery, as defined in [9] and [6], is a one-parameter metric deformation of a Riemannian manifold M , which stretches M across a separating hypersurface H in a cylindrical fashion; the singular limit is a complete manifold with asymptotically cylindrical ends, M . In this paper, the analysis of [9] and [6] is used to study the behaviour of analytic torsion of unitary representations under analytic surgery. A gluing formula is obtained relating the analytic torsion of M to the 'b-analytic torsion' b T (a regularized analytic torsion on manifolds with boundary) of M . This is then used to prove the Cheeger-Müller theorem, asserting the equality of analytic and Reidemeister torsion τ on closed manifolds, and to prove the following combinatorial formula for b-analytic torsion on odd dimensional manifolds with boundary:As a step in the proof, a Hodge-theoretic description of the Mayer-Vietoris sequence for cohomology under analytic surgery is developed.

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Self-adjoint elliptic operators and manifold decompositions part I: Low Eigenmodes and stretching

Cited by 39 publications

References 16 publications

Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

Positive scalar curvature, diffeomorphisms and the Seiberg–Witten invariants

Analytic surgery and analytic torsion

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