@unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On the index formula for singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116}, year = {1997}, abstract = {In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of elliptic operators on manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096}, year = {1997}, abstract = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.}, language = {en} } @unpublished{SchulzeTarkhanov1997, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The Riemann-Roch theorem for manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051}, year = {1997}, abstract = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.}, language = {en} }