3 definitions of BF theory on homology 3-spheres

On the Homology Cobordism Group of Homology 3-spheres

In this paper we present our results on the homology cobordism group Θ3Z of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and Seiberg – Witten. A closed oriented 3-manifold Σ is said to be an integral homology sphere if it has the same integral homology as the 3-sphere S. T...

The Seiberg-witten Theory of Homology 3-spheres

Seiberg-Witten-Floer Theory for Homology 3-Spheres

We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relative Seiberg-Witten invariants are applied to certain homology spheres boundin...

Unified So(3) Quantum Invariants for Rational Homology 3–spheres

Let M be a rational homology 3–sphere with |H1(M,Z)| = b. For any odd divisor c of b, we construct a unified invariant IM,c lying in a cyclotomic completion of a certain polynomial ring, which dominates Witten–Reshetikhin–Turaev SO(3) invariants of M at all roots of unity whose order r satisfies (r, b) = c. For c = 1, we recover the unified invariant constructed by Le and Beliakova–Le. If b = 1...

Seifert Fibered Homology 3 - Spheres Mike Krebs

To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3-sphere into the Lie group U(2, 1), we associate a real number called the “orbifold Toledo invariant.” Using the theory of Higgs bundles, we explicitly compute all values this invariant takes on.