ar X iv : 0 70 5 . 41 66 v 1 [ m at h . G T ] 2 9 M ay 2 00 7 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS

ar X iv : 0 70 5 . 41 66 v 2 [ m at h . G T ] 1 2 Ju n 20 07 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS

We present a short complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: Let M be a connected oriented closed smooth 3-manifold, L1(M) be the set of framed links in M up to a framed cobordism, and deg : L1(M) → H1(M ;Z) be the map taking a framed link to its homology class. Then for each α ∈ H1(M ;Z) there is a 1-1 corr...

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 : m at h - ph / 0 60 50 74 v 1 2 9 M ay 2 00 6 BRYANT - SALAMON ’ S G 2 - MANIFOLDS AND THE HYPERSURFACE GEOMETRY

We show that two of Bryant-Salamon’s G2-manifolds have a simple topology, S \ S or S \ CP . In this connection, we show there exists a complete Ricci-flat (non-flat) metric on Sn \ Sm for some n − 1 > m. We also give many examples of special Lagrangian submanifolds of T ∗Sn with the Stenzel metric. The hypersurface geometry is essential in the argument.

ar X iv : m at h / 05 05 66 9 v 1 [ m at h . D G ] 3 1 M ay 2 00 5 INVARIANT RIEMANNIAN METRICS AND f - STRUCTURES ON FLAG MANIFOLDS

It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...

ar X iv : h ep - t h / 03 05 03 7 v 2 3 0 M ay 2 00 3 FORMS ON VECTOR BUNDLES OVER COMPACT REAL HYPERBOLIC MANIFOLDS

We study gauge theories based on abelian p− forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.