Fixing the functoriality of Khovanov homology
D Clark, S Morrison, K Walker - Geometry & Topology, 2009 - msp.org
Fixing the functoriality of Khovanov homology Page 1 Geometry & Topology 13 (2009) 1499–1582
1499 Fixing the functoriality of Khovanov homology DAVID CLARK SCOTT MORRISON KEVIN …
1499 Fixing the functoriality of Khovanov homology DAVID CLARK SCOTT MORRISON KEVIN …
A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds
C Manolescu, M Marengon, S Sarkar… - Duke Mathematical …, 2023 - projecteuclid.org
We extend the definition of Khovanov–Lee homology to links in connected sums of S 1× S
2's and construct a Rasmussen-type invariant for null-homologous links in these manifolds …
2's and construct a Rasmussen-type invariant for null-homologous links in these manifolds …
Immersed curves in Khovanov homology
A Kotelskiy, L Watson, C Zibrowius - arXiv preprint arXiv:1910.14584, 2019 - arxiv.org
We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles
in the 3-ball with four ends: we associate with such 4-ended tangles $ T $ multicurves …
in the 3-ball with four ends: we associate with such 4-ended tangles $ T $ multicurves …
Khovanov homotopy type, Burnside category and products
We give a new construction of a Khovanov stable homotopy type, or spectrum. We show that
this construction gives a space stably homotopy equivalent to the Khovanov spectra …
this construction gives a space stably homotopy equivalent to the Khovanov spectra …
Khovanov homology and rational unknotting
D Iltgen, L Lewark, L Marino - arXiv preprint arXiv:2110.15107, 2021 - arxiv.org
Building on work by Alishahi-Dowlin, we extract a new knot invariant $\lambda\ge 0$ from
universal Khovanov homology. While $\lambda $ is a lower bound for the unknotting …
universal Khovanov homology. While $\lambda $ is a lower bound for the unknotting …
A topological quantum field theory approach to graph coloring
S Baldridge, B McCarty - arXiv preprint arXiv:2303.12010, 2023 - arxiv.org
In this paper, we use a topological quantum field theory (TQFT) to define families of new
homology theories of a $2 $-dimensional CW complex of a smooth closed surface. The …
homology theories of a $2 $-dimensional CW complex of a smooth closed surface. The …
ON KHOVANOV'S COBORDISM THEORY FOR KNOT HOMOLOGY
S Morrison, A Nieh - Journal of Knot Theory and its Ramifications, 2008 - World Scientific
We reconsider the link homology theory defined by Knovanov in [9] and generalized by
Mackaay and Vaz in [15]. With some slight modifications, we describe the theory as a map …
Mackaay and Vaz in [15]. With some slight modifications, we describe the theory as a map …
An odd Khovanov homotopy type
S Sarkar, C Scaduto, M Stoffregen - Advances in Mathematics, 2020 - Elsevier
For each link L⊂ S 3 and every quantum grading j, we construct a stable homotopy type X oj
(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜ …
(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜ …
A perturbation of the geometric spectral sequence in Khovanov homology
We study the relationship between Bar-Natan's perturbation in Khovanov homology and
Szabó's geometric spectral sequence, and construct a link invariant that generalizes both …
Szabó's geometric spectral sequence, and construct a link invariant that generalizes both …
Khovanov homology
LH Kauffman - Introductory Lectures on Knot Theory, Ser. Knots …, 2011 - books.google.com
Khovanov homology Page 263 248 KHOVANOV HOMOLOGY Louis H. Kauffman Department
of Mathematics, Statistics and Computer Science (m/c 249) 851 South Morgan Street University …
of Mathematics, Statistics and Computer Science (m/c 249) 851 South Morgan Street University …