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Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups

Jérôme Dubois (2005)

Annales de l’institut Fourier

For a knot K in the 3-sphere and a regular representation of its group G K into SU(2) we construct a non abelian Reidemeister torsion form on the first twisted cohomology group of the knot exterior. This non abelian Reidemeister torsion form provides a volume form on the SU(2)-representation space of G K . In another way, we construct using Casson’s original construction a natural volume form on the SU(2)-representation space of G K . Next, we compare these two apparently different points of view on the representation...

Non equivalence of NMS flows on S 3

B. Campos, P. Vindel (2012)

Mathematica Bohemica

We build the flows of non singular Morse-Smale systems on the 3-sphere from its round handle decomposition. We show the existence of flows corresponding to the same link of periodic orbits that are non equivalent. So, the link of periodic orbits is not in a 1-1 correspondence with this type of flows and we search for other topological invariants such as the associated dual graph.

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

Let A be a dg algebra over 𝔽 2 and let M be a dg A -bimodule. We show that under certain technical hypotheses on A , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product M ⊗ A L M and converges to the Hochschild homology of M . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

Nonfibered knots and representation shifts

Daniel S. Silver, Susan G. Williams (2009)

Banach Center Publications

A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.

Non-slice linear combinations of algebraic knots

Matthew Hedden, Paul Kirk, Charles Livingston (2012)

Journal of the European Mathematical Society

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.

Non-standard automorphisms of branched coverings of a disk and a sphere

Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb (2012)

Fundamenta Mathematicae

Let Y be a closed 2-dimensional disk or a 2-sphere. We consider a simple, d-sheeted branched covering π: X → Y. We fix a base point A₀ in Y (A₀ ∈ ∂Y if Y is a disk). We consider the homeomorphisms h of Y which fix ∂Y pointwise and lift to homeomorphisms ϕ of X-the automorphisms of π. We prove that if Y is a sphere then every such ϕ is isotopic by a fiber-preserving isotopy to an automorphism which fixes the fiber π - 1 ( A ₀ ) pointwise. If Y is a disk, we describe explicitly a small set of automorphisms of...

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