1 99 6 Twisted L 2 Invariants of Non - Simply Connected Manifolds and Asymptotic L 2 Morse Inequalities

Twisted L2 Invariants of Non-simply Connected Manifolds and Asymptotic L2 Morse Inequalities

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

Invariants of Non - Simply Connectedmanifolds and Asymptotic L 2 Morse Inequalities

Seiberg-witten-floer Homology of a Surface times a Circle

We determine the Seiberg–Witten–Floer homology groups of the 3-manifold Σ × S 1, where Σ is a surface of genus g � 2, together with its ring structure, for a Spin� structure with non-vanishing first Chern class. We give applications to computing Seiberg–Witten invariants of 4-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities obtained b...

Novikov Inequalities with Symmetry

We suggest Novikov type inequalities in the situation of a compact Lie groups action assuming that the given closed 1-form is invariant and basic. Our inequalities use equivariant cohomology and an appropriate equivariant generalization of the Novikov numbers. We test and apply our inequalities in the case of a finite group. As an application we obtain Novikov type inequalities for a manifold w...

The Donaldson-Witten function for gauge groups of rank larger than one

We study correlation functions in topologically twisted N = 2, d = 4 supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds X . We find that the topological invariance of the generator of correlation functions of BRST invariant observables is not spoiled by noncompactness of field space. We show how to express the correlators on simply connected mani...