This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group S n on the cohomology of the configuration space of n ordered points in R d. This cohomology is known to vanish outside of dimensions divisible by d − 1; it is shown here that the S n-representation on the i(d − 1)st coho-mology stabilizes sharply at n = 3i (resp. n = 3i + 1) w...

Abstract We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the triple linking number from link complex, detection results Whitehead Borromean rings, structural property of $d$-invariants surgeries on certain algebraically split links.

Nanobody (Nb) or VHH is the smallest binding domain of camelid heavy chain antibody (HcAb). Light chains of HcAb naturally removed and because of some evolutionary changes, Nbs have unique properties rather than conventional antibodies. The size of Nb is about one-tenth (0.1) of whole antibodies and this size improved some problems of four chains antibodies such as high yield of expression in p...

Abstract We show that the triply graded Khovanov–Rozansky homology of knots and links over a field positive odd characteristic p descends to an invariant in homotopy category finite-dimensional -complexes. A -extended differential on discovered by Cautis is compatible with -DG structure. As consequence, we get categorification Jones polynomial evaluated at $2p$ th root unity.

where H;(_) denotes the Lie algebra homology, HC*(_) cyclic homology, and A is an algebra with unit over a field of characteristic zero. In this paper we give an alternative proof of this theorem which does not involve Weyl's invariant theory for GL(C). We use this approach to compute Chevalley-Eilenberg homology in some interesting new cases. In Section 1, we begin by proving (in characteristi...

D-branes are classified by twisted K-theory. Yet twisted K-theory is often hard to calculate. We argue that, in the case of a compactification on a simply-connected six manifold, twisted K-theory is isomorphic to a much simpler object, twisted homology. Unlike K-theory, homology can be twisted by a class of any degree and so it classifies not only D-branes but also M-branes. Twisted homology cl...

A bstract: The seeding technique became central in the theory of sequence alignment and there are several efficient tools applying seeds to D N A homology search. Recently, a concept of subset seeds has been proposed for similarity search in protein sequences. We experimentally evaluate the applicability of subset seeds to protein homology search. We advocate the use of multiple subset seeds de...

This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group Sn on the cohomology of the configuration space of n ordered points in R. This cohomology is known to vanish outside of dimensions divisible by d− 1; it is shown here that the Sn-representation on the i(d− 1) cohomology stabilizes sharply at n = 3i (resp. n = 3i + 1) when d is ...