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- STEFAN FRIEDL
- 2003

We classify the metabelian unitary representations of π 1 (M K), where M K is the result of zero-surgery along a knot K ⊂ S 3. We show that certain eta invariants associated to metabelian representations π 1 (M K) → U (k) vanish for slice knots and that even more eta invariants vanish for ribbon knots and doubly slice knots. We show that this result… (More)

In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group Z that does not split off S 1 × S 3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain… (More)

- STEFAN FRIEDL, TAEHEE KIM
- 2005

Every element in the first cohomology group of a 3–manifold is dual to embedded surfaces. The Thurston norm measures the minimal 'complexity' of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the knot in the 3–sphere. We show that the degrees of twisted Alexander polynomials give lower bounds on the Thurston norm,… (More)

- STEFAN FRIEDL, STEFANO VIDUSSI
- 2009

We give a short introduction to the theory of twisted Alexander polynomials of a 3–manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted Reidemeister torsion. We then give a survey of the many applications of twisted invariants to the study of topological problems.… (More)

- STEFAN FRIEDL, STEFANO VIDUSSI
- 2006

Let N be a closed, oriented 3–manifold. A folklore conjecture states that S 1 × N admits a symplectic structure only if N admits a fibration over the circle. The purpose of this paper is to provide evidence to this conjecture studying suitable twisted Alexander polynomials of N , and showing that their behavior is the same as of those of fibered 3–… (More)

T T T T T T T T T T T T T T T Abstract In the early 1980's Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group Z). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficient homological condition under which a knot is slice with fundamental group Z… (More)

- STEFAN FRIEDL, TAEHEE KIM
- 2005

We introduce twisted Alexander norms of a compact connected ori-entable 3-manifold with first Betti number bigger than one generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many 3-manifolds which can not be… (More)

- STEFAN FRIEDL
- 2003

We study the eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha–Ko. We give a formula for the eta-invariant for boundary links. In several intersting cases this allows us to show… (More)

- STEFAN FRIEDL
- 2008

Cochran introduced Alexander polynomials over non–commutative Lau-rent polynomial rings. Their degrees were studied by Cochran, Harvey and Turaev as they give lower bounds on the Thurston norm. We first extend Cochran's definition to twisted Alexander polynomials. We then show how Reidemeister torsion relates to these invariants and we give lower bounds on… (More)

- STEFAN FRIEDL, STEFANO VIDUSSI
- 2007

In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguishing knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial knots. Furthermore building on results… (More)