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Index formulas on stratified manifolds ∗
, 2008
"... Elliptic operators on stratified manifolds with any finite number of strata are considered. Under certain assumptions on the symbols of operators, we obtain index formulas, which express index as a sum of indices of elliptic operators on the strata. 1 ..."
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Elliptic operators on stratified manifolds with any finite number of strata are considered. Under certain assumptions on the symbols of operators, we obtain index formulas, which express index as a sum of indices of elliptic operators on the strata. 1
An index formula for simple graphs
, 2012
"... Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x) is ..."
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Cited by 7 (7 self)
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Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x
The equivariant index formula on orbifolds
 Duke Math. J
, 1996
"... acting on P. We assume that the action of H is infinitesimally free, that is, the stabilizer H(y) of any point y e P is a finite subgroup of H. We write the action of H on the right. The quotient space P/H is an orbifold. (If H acts freely, then P/H is a manifold.) Reciprocally, any orbifold M can b ..."
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Cited by 16 (1 self)
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acting on P. We assume that the action of H is infinitesimally free, that is, the stabilizer H(y) of any point y e P is a finite subgroup of H. We write the action of H on the right. The quotient space P/H is an orbifold. (If H acts freely, then P/H is a manifold.) Reciprocally, any orbifold M can be presented this way: for
On index formulas for manifolds with metric horns
, 1999
"... In this paper we discuss the index problem for geometric differential operators (Spin–Dirac operator, GaußBonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have unique closed extensions. But there always exist two extremal e ..."
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Cited by 11 (0 self)
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extensions Dmin and Dmax. We describe the quotient D(Dmax)/D(Dmin) explicitely in geometric resp. topological terms of the base manifolds of the metric horns. We derive index formulas for the Spin–Dirac and GaußBonnet operator. For the Signature operator we present a partial result.
INDEX FORMULAE FOR STARK UNITS AND THEIR SOLUTIONS
 PACIFIC JOURNAL OF MATHEMATICS
, 2013
"... Let K/k be an abelian extension of number fields with a distinguished place of k that splits totally in K. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in K, called the Stark unit, constructed from the values of the Lfunctions attached to the extension. ..."
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. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, we study the solutions of the index formulae and prove that they admit solutions unconditionally for quadratic, quartic and sextic (with some additional conditions) cyclic extensions. As a result we deduce a weak
A local families index formula for . . .
, 2009
"... Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of ∂operators on the Teichmüller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space Mg,n in the sense of orbifolds where it can be written in te ..."
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Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of ∂operators on the Teichmüller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space Mg,n in the sense of orbifolds where it can be written
The local index formula for quantum SU(2)
, 2006
"... The local index formula of Connes–Moscovici for the isospectral noncommutative geometry recently constructed on quantum SU(2) [14, 20] is discussed. The cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula, are presented. ..."
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The local index formula of Connes–Moscovici for the isospectral noncommutative geometry recently constructed on quantum SU(2) [14, 20] is discussed. The cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula, are presented.
Results 1  10
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623,086