Geodesic
On bordered theories for Khovanov homology
Manion, Andrew1
1Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1557-1674
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We describe how to formulate Khovanov’s functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts’ type D and type A structures in Khovanov homology, and his algebra ℬΓn, in terms of Khovanov’s theory of modules over the ring Hn. We reprove invariance and pairing properties of Roberts’ bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of Hn which may be of independent interest.

DOI : 10.2140/agt.2017.17.1557
Classification : 57M27
Keywords: Khovanov homology, bordered Floer homology, invariants of tangles, linear-quadratic algebras

Manion, Andrew  1

1 Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, United States 
@article{10_2140_agt_2017_17_1557,
     author = {Manion, Andrew},
     title = {On bordered theories for {Khovanov} homology},
     journal = {Algebraic and Geometric Topology},
     pages = {1557--1674},
     year = {2017},
     volume = {17},
     number = {3},
     doi = {10.2140/agt.2017.17.1557},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1557/}
}
TY  - JOUR
AU  - Manion, Andrew
TI  - On bordered theories for Khovanov homology
JO  - Algebraic and Geometric Topology
PY  - 2017
SP  - 1557
EP  - 1674
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1557/
DO  - 10.2140/agt.2017.17.1557
ID  - 10_2140_agt_2017_17_1557
ER  - 
%0 Journal Article
%A Manion, Andrew
%T On bordered theories for Khovanov homology
%J Algebraic and Geometric Topology
%D 2017
%P 1557-1674
%V 17
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1557/
%R 10.2140/agt.2017.17.1557
%F 10_2140_agt_2017_17_1557
Manion, Andrew. On bordered theories for Khovanov homology. Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1557-1674. doi: 10.2140/agt.2017.17.1557

[1] R M Adin, Y Roichman, On maximal chains in the non-crossing partition lattice, J. Combin. Theory Ser. A 125 (2014) 18 | DOI

[2] D Bessis, The dual braid monoid, Ann. Sci. École Norm. Sup. 36 (2003) 647 | DOI

[3] T Braden, Perverse sheaves on Grassmannians, Canad. J. Math. 54 (2002) 493 | DOI

[4] M Khovanov, A functor-valued invariant of tangles, Algebr. Geom. Topol. 2 (2002) 665 | DOI

[5] R Lipshitz, P Ozsvath, D Thurston, Bordered Heegaard Floer homology: invariance and pairing, preprint (2008)

[6] R Lipshitz, P S Ozsváth, D P Thurston, Heegaard Floer homology as morphism spaces, Quantum Topol. 2 (2011) 381

[7] R Lipshitz, P S Ozsváth, D P Thurston, Bimodules in bordered Heegaard Floer homology, Geom. Topol. 19 (2015) 525 | DOI

[8] A J Manion, Constructions and computations in Khovanov homology, PhD thesis, Princeton Universty (2015)

[9] D Pálvölgyi, For any two noncrossing partitions p,q of n, is the graph of geodesics from p to q in NC(n) connected ?,

[10] A Polishchuk, L Positselski, Quadratic algebras, 37, Amer. Math. Soc. (2005) | DOI

[11] L Roberts, A type A structure in Khovanov homology, Algebr. Geom. Topol. 16 (2016) 3653 | DOI

[12] L P Roberts, A type D structure in Khovanov homology, Adv. Math. 293 (2016) 81 | DOI

[13] C Stroppel, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, Compos. Math. 145 (2009) 954 | DOI

Cité par Sources :