Rational Homology 7-Spheres
نویسندگان
چکیده
In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.
منابع مشابه
Einstein Metrics on Rational Homology Spheres
In this paper we prove the existence of Einstein metrics, actually SasakianEinstein metrics, on nontrivial rational homology spheres in all odd dimensions greater than 3. It appears as though little is known about the existence of Einstein metrics on rational homology spheres, and the known ones are typically homogeneous. The are two exception known to the authors. Both involve Sasakian geometr...
متن کاملOn Finite Type 3-manifold Invariants V: Rational Homology 3-spheres
We introduce a notion of nite type invariants of oriented rational homology 3-spheres. We show that the map to nite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of nite type invari-ants of rational homology 3-spheres is a ltered commutative algebra with nite dimensional nonzero graded quotients only in degrees divisible by 3. We show that the Casson-Wal...
متن کاملSignatures of Links in Rational Homology Spheres
A theory of signatures for odd-dimensional links in rational homology spheres are studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate 1-dimensional links with mutual linking. Furthermore our concordant theory of links in rational homology spheres remains highly...
متن کاملThe Perturbative Invariants of Rational Homology 3-spheres Can Be Recovered from the Lmo Invariant the Perturbative Invariants of Rational Homology 3-spheres Can Be Recovered from the Lmo Invariant
We show that the perturbative g invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra g, i.e., the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13, 14, 15], this implies that the LMO in...
متن کاملAn equivariant Casson invariant of knots in homology spheres
From the construction of the Casson invariant of homology spheres using intersection on configuration spaces, we propose a construction of an equivariant Casson invariant for a knot K homologous to 0 in rational homology sphere M . Our construction is adapted from C. Lescop ([7]) and use the same ideas in an equivariant setting. We show that the invariant we obtain is similar to the 2-loop part...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008