A lattice of finite-type invariants of virtual knots

Micah W. Chrisman

Banach Center Publications (2014)

  • Volume: 100, Issue: 1, page 27-49
  • ISSN: 0137-6934

Abstract

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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 knots, all of which satisfy the same skein relation. Bounds for the rank of each group in the lattice are obtained.

How to cite

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Micah W. Chrisman. "A lattice of finite-type invariants of virtual knots." Banach Center Publications 100.1 (2014): 27-49. <http://eudml.org/doc/282569>.

@article{MicahW2014,
abstract = {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 knots, all of which satisfy the same skein relation. Bounds for the rank of each group in the lattice are obtained.},
author = {Micah W. Chrisman},
journal = {Banach Center Publications},
keywords = {Polyak algebra; finite type invariants; virtual knots},
language = {eng},
number = {1},
pages = {27-49},
title = {A lattice of finite-type invariants of virtual knots},
url = {http://eudml.org/doc/282569},
volume = {100},
year = {2014},
}

TY - JOUR
AU - Micah W. Chrisman
TI - A lattice of finite-type invariants of virtual knots
JO - Banach Center Publications
PY - 2014
VL - 100
IS - 1
SP - 27
EP - 49
AB - 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 knots, all of which satisfy the same skein relation. Bounds for the rank of each group in the lattice are obtained.
LA - eng
KW - Polyak algebra; finite type invariants; virtual knots
UR - http://eudml.org/doc/282569
ER -

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