ETA INVARIANTS FOR MANIFOLD WITH BOUNDARY

Let M be a 3-manifold with boundary ∂M. Let X be a C∞, vector field on M, tangent to ∂M, exhibiting a singular cycle associated to a hyperbolic equilibrium σ∈∂M with real eigenvalues λss < λs < 0 < λu satisfying λs - λss - 2λu > 0. We prove under generic conditions and k large enough the existence of a Ck robust transitive set of X, that is, any Ck vector field Ck close to X exhibits a transitive set containing the cycle. In particular, C∞ vector fields exhibiting Ck robust transitive sets, for k large enough, which are not singular-hyperbolic do exist on any compact 3-manifold with boundary.

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The gradient estimate of a Neumann eigenfunction on a compact manifold with boundary

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-015-0924-6 ◽

2015 ◽

Vol 36 (6) ◽

pp. 991-1000 ◽

Cited By ~ 1

Author(s):

Jingchen Hu ◽

Yiqian Shi ◽

Bin Xu

Keyword(s):

Compact Manifold ◽

Gradient Estimate ◽

Manifold With Boundary

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Eleven-dimensional supergravity on a manifold with boundary

Nuclear Physics B ◽

10.1016/0550-3213(96)00308-2 ◽

1996 ◽

Vol 475 (1-2) ◽

pp. 94-114 ◽

Cited By ~ 1100

Author(s):

Petr Hořava ◽

Edward Witten

Keyword(s):

Manifold With Boundary

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CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

Glasgow Mathematical Journal ◽

10.1017/s0017089518000502 ◽

2018 ◽

Vol 62 (1) ◽

pp. 13-41

Author(s):

MICHAEL S. WEISS

Keyword(s):

Compact Manifold ◽

Geometric Conditions ◽

Homeomorphism Group ◽

Manifold With Boundary ◽

Smooth Compact Manifold

AbstractLet M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

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Spectral Flow in Fredholm Modules, Eta Invariants and the JLO Cocycle

K-Theory ◽

10.1023/b:kthe.0000022922.68170.61 ◽

2004 ◽

Vol 31 (2) ◽

pp. 135-194 ◽

Cited By ~ 27

Author(s):

Alan Carey ◽

John Phillips

Keyword(s):

Spectral Flow ◽

Eta Invariants

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QUANTUM LIOUVILLE FIELD THEORY ON A MANIFOLD WITH BOUNDARY

Modern Physics Letters A ◽

10.1142/s0217732398002175 ◽

1998 ◽

Vol 13 (25) ◽

pp. 2057-2063

Author(s):

S. A. APIKYAN

Keyword(s):

Field Theory ◽

Functional Equations ◽

Ward Identity ◽

Semiclassical Approximation ◽

Boundary Structure ◽

Manifold With Boundary ◽

Structure Constants ◽

Liouville Field Theory

This letter studies the quantum Liouville field theory on a manifold with boundary. The boundary conformal Ward identity (CWI) is written and its semiclassical approximation is analyzed. This establishes a method of finding the accessory parameters of the theory with boundary. The boundary structure constants of the theory are defined and the functional equations which determine them are derived.

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