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B Ćaćić (2012)
A reconstruction theorem for almost-commutative spectral triplesLett. Math. Phys., 100
D Buchholz, R Longo (1999)
Graded KMS-functionals and the breakdown of supersymmetryAdv. Theor. Math. Phys., 3
E Ha, F Paugam (2005)
Bost-Connes-Marcolli systems for Shimura varieties. I. Definitions and formal analytic propertiesIMRP Int. Math. Res. Pap., 5
M A Rieffel (2004)
Compact quantum metric spacesOperator Algebras, Quantization, and Noncommutative Geometry, 365
D Spector (1998)
Duality, partial supsersymmetry, and arithmetic number theoryJ. Math. Phys., 39
D Spector (1990)
Supersymmetry and the Möbius inversion functionCommun. Math. Phys., 127
J W Jong (2009)
Graphs, spectral triples and Dirac zeta functionsp-Adic Numbers Ultrametric Anal. Appl., 1
A Connes (2013)
On the spectral characterization of manifoldsJ. Noncomm. Geom., 7
A Connes (1994)
Noncommutative Geometry
A Connes, H Moscovici (1995)
The local index formula in noncommutative geometryGeom. Funct. Anal., 5
D Sullivan (1979)
The density at infinity of a discrete group of hyperbolic motionsInst. Hautes Études Sci. Publ. Math., 50
S J Patterson (1976)
The limit set of a Fuchsian groupActa Math., 136
A Connes, M Marcolli (2008)
An Invitation to Noncommutative Geometry
P B Gilkey (2004)
Asymptotic Formulae in Spectral Geometry
S Cecotti, L Girardello (1982)
Functional measure, topology, and dynamical supersymmetry breakingPhys. Lett. B, 110
A Chamseddine, A Connes, M Marcolli (2007)
Gravity and the standard model with neutrino mixingAdv. Theor. Math. Phys., 11
A Connes (2008)
A unitary invariant in Riemannian geometryInt. J. Geom. Meth. Mod. Phys., 5
J Lott (2005)
Limit sets as examples in noncommutative geometryK-Theory, 34
D Kastler (1989)
Cyclic cocycles from graded KMS functionalsCommun. Math. Phys., 121
M Laca, I Raeburn (1999)
A semigroup crossed product arising in number theoryJ. London Math. Soc. (2), 59
A Connes, H Moscovici (2008)
Type III and spectral triplesTraces in Number Theory, Geometry and Quantum Fields, 38
O Stoytchev (1993)
The modular group and super-KMS functionalsLett. Math. Phys., 27
A Connes (1995)
Geometry from the spectral point of viewLett. Math. Phys., 34
G Cornelissen, M Marcolli (2008)
Zeta functions that hear the shape of a Riemann surfaceJ. Geom. Phys., 58
S Lord, A Rennie, J C Varilly (2012)
Riemannian manifolds in noncommutative geometryJ. Geom. Phys., 62
A Connes, M Marcolli, N Ramachandran (2005)
KMS states and complex multiplicationSelecta Math. (N.S.), 11
R Akhoury, A Comtet (1984)
Anomalous behavior of the Witten index — exactly soluble modelsNucl. Phys. B, 246
M Laca, N Larsen, S Neshveyev (2009)
On Bost-Connes types systems for number fieldsJ. Number Theory, 129
M Coornaert (1993)
Mesures de Patterson-Sullivan sur le bord d’un espace hyperbolique au sens de GromovPacific J. Math., 159
A Jaffe (1988)
The Legacy of John von Neumann
G Cornelissen, J W Jong (2012)
The spectral length of a map between Riemannian manifoldsJ. Noncomm. Geom., 6
J B Bost, A Connes (1995)
Hecke algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theorySelecta Math., 1
A Connes (1989)
Compact metric spaces, Fredholm modules, and hyperfinitenessErgod. Th. Dynam. Sys., 9
N Higson, J Roe (2000)
Analytic K-Homology
A Chamseddine, A Connes (1997)
The spectral action principleComm. Math. Phys., 186
E Witten (1982)
Constraints on supersymmetry breakingNucl. Phys. B, 202
B Julia (1990)
Number Theory and Physics
Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of twisted spectral triple, introduced recently by Connes and Moscovici, provides a natural bridge between them. We investigate explicit examples, related to the Bost-Connes quantum statistical mechanical system and to Riemann surfaces and graphs.
P-Adic Numbers, Ultrametric Analysis, and Applications – Springer Journals
Published: May 7, 2014
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