Homology of coloured posets: a generalisation of Khovanov’s cube construction
نویسنده
چکیده
We generalise Khovanov’s chain complex built from a “cube” of modules and homomorphisms, to a more general setting. We define the notion of a coloured poset and construct a homology functor for these objects, showing that for coloured Boolean lattices the resulting homology agrees with the homology of Khovanov’s complex.
منابع مشابه
Bundles of coloured posets and a Leray-Serre spectral sequence
A coloured poset is a poset with a unique maximal element that is equipped with a sheaf of modules. In this paper we initiate the study of a bundle theory for coloured posets, producing for a certain class of base posets a LeraySerre type spectral sequence. We then show how this theory finds application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homolog...
متن کاملOdd Khovanov Homology
We describe an invariant of links in S which is closely related to Khovanov’s Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov’s definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones ...
متن کاملSemi-pointed partition posets and Species
We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and the character for the action of the symmetric groups on their homology. We finally study the associated incidence Hopf algebra, which is similar to the Faà di Bruno Hopf algebra.
متن کاملTopology of eigenspace posets for imprimitive reflection groups
This paper studies the poset of eigenspaces of elements of an imprimitive unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. The study of this poset is suggested by the eigenspace theory of Springer and Lehrer. The posets are shown to be isomorphic to certain subposets of Dowling lattices (the ”d-divisible, k-evenly coloured Dowling lattices”). This enables u...
متن کاملTHE UNIVERSAL sl3-LINK HOMOLOGY
We define the universal sl3-link homology, which depends on 3 parameters, following Khovanov’s approach with foams. We show that this 3parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov’s original sl3-link homology belongs, the second is the one studied by Gornik in the context of matrix factoriz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007