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A homological selection theorem implying a division theorem for Q-manifolds

Taras Banakh, Robert Cauty (2007)

Banach Center Publications

We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...

A Lagrangian representation of tangles II

David Cimasoni, Vladimir Turaev (2006)

Fundamenta Mathematicae

The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.

A lattice of finite-type invariants of virtual knots

Micah W. Chrisman (2014)

Banach Center Publications

We construct an infinite commutative lattice of groups whose dual spaces give Kauffman finite-type invariants of long virtual knots. The lattice is based "horizontally" upon the Polyak algebra and extended "vertically" using Manturov's functorial map f. For each n, the n-th vertical line in the lattice contains an infinite-dimensional subspace of Kauffman finite-type invariants of degree n. Moreover, the lattice contains infinitely many inequivalent extensions of the Conway polynomial to long virtual...

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