8 papers
Casson--type invariants in dimension four
Daniel Ruberman, Nikolai Saveliev
This article surveys our ongoing project about the relationship between invariants extending the classical Rohlin invariant of homology spheres and those coming from 4-dimensional…
Rohlin's invariant and gauge theory, I. Homology 3-tori
Daniel Ruberman, Nikolai Saveliev
This is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the inte…
The Seiberg-Witten invariants of manifolds with wells of negative curvature
Daniel Ruberman
We extend the vanishing theorem for the Seiberg-Witten invariants of a manifold with positive scalar curvature to the case when the curvature is allowed to be negative on a set of…
Mod 2 Seiberg-Witten invariants of homology tori
Daniel Ruberman, Saso Strle
We show that the mod 2 Seiberg-Witten invariant can be determined for a spin manifold X which has the same homology groups as the 4-torus. The value depends on the structure of the…
Embedding tangles in links
Daniel Ruberman
We reprove and extend a result of David Krebes (J. Knot Theory Ramif. 8 (1999), 321-352) giving an obstruction to embedding a tangle T into a link L. Closing the tangle up in the t…
An obstruction to smooth isotopy in dimension 4
Daniel Ruberman
Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly is…