We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-11,
author = {Sam Nelson},
title = {Link invariants from finite racks},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {243-258},
zbl = {1297.57018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-11}
}
Sam Nelson. Link invariants from finite racks. Fundamenta Mathematicae, Tome 227 (2014) pp. 243-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-11/