Self-adjoint local boundary problems on compact surfaces. I. Spectral flow

The paper deals with first order self-adjoint elliptic differential operators on a smooth compact oriented surface with non-empty boundary. We consider such operators with self-adjoint local boundary conditions. The paper is focused on paths in the space of such operators connecting two operators conjugated by a unitary automorphism. The first result is the computation of the spectral flow for such paths in terms of the topological data over the boundary. The second result is the universality of the spectral flow: we show that the spectral flow is a universal additive invariant for such paths, if the vanishing on paths of invertible operators is required. In the next paper of the series we generalize these results to families of such operators parametrized by points of an arbitrary compact space instead of an interval. The integer-valued spectral flow is replaced then by the family index taking values in the $K^1$-group of the base space.Comment: 46 pages. V4: minor changes; version accepted by the Journal of Geometric Analysi

A Stability Pact for the Caucasus in Theory and Practice - A Supplementary Note. CEPS Working Document No. 152, September 2000

In response to appeals of the leaders of the South Caucasus for a Stability Pact for the region, CEPS published in May 2000 a consultative document with a comprehensive proposal (available on www.ceps.be). Subsequently the authors have held extensive consultations with the leaders in all three states of the South Caucasus, and in four of the key autonomies (Nagorno Karabakh, Abkhazia, Adjaria, Ossetia). The present paper draws together the information and ideas collected during these consultations, although the conclusions are only attributable to the authors. The main argument of the original document is maintained, and strengthened with more precise views on how the conflicts might be solved within the framework of a Stability Pact. However the proposed Stability Pact process could be more than just an approach to conflict resolution. It has systemic or even constitutional aspects, with elements to overcome the transitional problems of the weak state and ease the confrontations of traditional notions such as independence versus territorial integrity, or the choice between federation and confederation, which are part of the present impasse. Particular consideration is also given to how a Caucasus Stability Pact could serve the interests of Russia as the region’s key player, together with enhanced cooperation with the EU over a Southern Dimension concept