Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant (2009)
Mrowka, Tomasz S., Ruberman, Daniel, Saveliev, Nikolai
We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of $S^1 \times S^3$. The invariant has two terms; one is a count of solutions to the...
Smooth surfaces with non-simply-connected complements (2008)
Kim, Hee Jung, Ruberman, Daniel
We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also...
A FAKE SMOOTH CP 2 #RP 4 (2008)
Abstract. We show that the manifold ∗CP 2 # ∗ RP 4, which is homotopy equivalent but not homeomorphic to CP 2 #RP 4, is in fact smoothable. 1.
A Sextic Surface Cannot Have 66 Nodes (2007)
David B. Jaffe, Daniel Ruberman
this paper, we complete the story by showing that S cannot have 66 nodes.
Daniel Ruberman, Ronald J. Stern
. We show that the manifold #CP 2 # # RP 4 , which is homotopy equivalent but not homeomorphic to CP 2 #RP 4 , is in fact smoothable. 1. Introduction In Kirby's problem list [Kir97, Problem...
Mathematik Departement ETH Zurich ETH-Zentrum (2007)
Bai Ling Wang, Shuguang Wang, Daniel Ruberman, Dietmar Salamon, Nikolai Saveliev, Birgit Schmidt, ...
Ramistr. 101
Dirac operators on manifolds with periodic ends (2007)
Ruberman, Daniel, Saveliev, Nikolai
This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a sufficient condition for such an operator to be Fredholm for a generic end-periodic metric;...
Knot concordance and Heegaard Floer homology invariants in branched covers (2007)
Grigsby, J. Elisenda, Ruberman, Daniel, Strle, Saso
By studying the Heegaard Floer homology of the preimage of a knot K in S^3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth...
Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles (2006)
Cha, Jae Choon, Livingston, Charles, Ruberman, Daniel
If the Bing double of a knot K is slice, then K is algebraically slice. In addition, Heegaard--Floer concordance invariants developed by Ozsvath-Szabo and by Manolescu-Owens vanish on K.
Topological triviality of smoothly knotted surfaces in 4-manifolds (2006)
Kim, Hee Jung, Ruberman, Daniel
Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then...
Casson--type invariants in dimension four (2005)
Ruberman, Daniel, Saveliev, Nikolai
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 (Yang-Mills) gauge...
Rohlin's invariant and gauge theory III. Homology 4--tori (2004)
Ruberman, Daniel, Saveliev, Nikolai
This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in...
Rohlin's invariant and gauge theory II. Mapping tori (2003)
Ruberman, Daniel, Saveliev, Nikolai
This is the second in a series of papers studying the relationship between Rohlin's theorem and gauge theory. We discuss an invariant of a homology S^1 cross S^3 defined by Furuta and Ohta as an...
Rohlin's invariant and gauge theory, I. Homology 3-tori (2003)
Ruberman, Daniel, Saveliev, Nikolai
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 integral homology of a...
The Seiberg-Witten invariants of manifolds with wells of negative curvature (2002)
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 small volume. (The...
Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants (2001)
We study the space of positive scalar curvature (psc) metrics on a 4-manifold, and give examples of simply connected manifolds for which it is disconnected. These examples imply that concordance of...
Mod 2 Seiberg-Witten invariants of homology tori (2000)
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 cohomology ring of...
Embedding tangles in links (2000)
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 two obvious ways...
A polynomial invariant of diffeomorphisms of 4-manifolds (1999)
We use a 1-parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4-manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and is...
An obstruction to smooth isotopy in dimension 4 (1998)
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 isotopic to the...
Isospectrality and 3-manifold groups (1997)
The relationship between the Chern-Simons invariant and eta-invariant of a 3-manifold is shown to lead to an obstruction to a group being the fundamental group of a closed oriented 3-manifold. The...
Mutation and Gauge Theory I: Yang-Mills Invariants (1997)
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to...
A fake smooth CP^2 # RP^4 (1997)
Ruberman, Daniel, Stern, Ronald J.
We show that the manifold *CP^2 # *RP^4, which is homotopy equivalent but not homeomorphic to CP^2 # RP^4, is in fact smoothable.
Daniel Ruberman, Ronald J. Stern
. We show that the manifold RP 4 # CP 2 , which is homotopy equivalent but not homeomorphic to RP 4 #CP 2 , is in fact smoothable. 1. Introduction In Kirby's problem list [Kir97, Problem 4.82]...
A sextic surface cannot have 66 nodes (1995)
Jaffe, David B., Ruberman, Daniel
Let S be a surface in complex projective 3-space, having only nodes as singularities. Suppose that S has degree 6. We show that the maximum number of nodes which S can have is 65. An abbreviated...
Doubly slice knots and the Casson-Gordon invariants / (1982)
Thesis (Ph. D.)--University of California, Berkeley, 1982.
Doubly slice knotsand the Casson-Gordon invariants / (1982)
Thesis (Ph. D. in Mathematics)--University of California, Berkeley, June 1982.