ar X iv : 0 70 5 . 38 12 v 1 [ m at h . D S ] 2 5 M ay 2 00 7 DYNAMICS OF THE TEICHMÜLLER FLOW ON COMPACT INVARIANT SETS

ar X iv : 0 70 5 . 38 12 v 2 [ m at h . D S ] 2 4 Ja n 20 08 DYNAMICS OF THE TEICHMÜLLER FLOW ON COMPACT INVARIANT SETS

Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is...

ar X iv : 0 70 5 . 10 42 v 1 [ m at h . M G ] 8 M ay 2 00 7 NON - POSITIVE CURVATURE AND THE PTOLEMY INEQUALITY

We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.

ar X iv : 0 70 5 . 12 53 v 1 [ m at h . A C ] 9 M ay 2 00 7 DUALITIES AND INTERSECTION MULTIPLICITIES

Let R be a commutative, noetherian, local ring. Topological Q– vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

ar X iv : 0 70 5 . 31 41 v 1 [ as tr o - ph ] 2 2 M ay 2 00 7 The SARG Planet Search

ar X iv : 0 80 4 . 14 18 v 2 [ m at h . D G ] 2 7 M ay 2 00 8 SMOOTH YAMABE INVARIANT AND SURGERY

We prove a surgery formula for the smooth Yamabe invariant σ(M) of a compact manifold M . Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positive constant Λn, depending only on the dimension n of M , such that σ(N) ≥ min{σ(M),Λn}.