We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a (2, n)-torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete connection. In the general case of Khovanov-Rozansky, sl(n), homology and their deforma...

Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each f. g. projective R/I-module V has an Rprojective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 → P0 for all n ≥ 1, if d = 1. This computation yields a new proof of the classical Adams-Riemann-R...

This article is based on the author’s talk at international conference dedicated to memory of Professor B. Yu. Sternin (Moscow, November 6–9, 2018). The Hochschild homology and cohomology a group algebra can be described via classifying space adjoint action groupoid under suitable assumption finiteness supports groups. difference between leads correction results in D. J. Benson’s book Represent...

Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and d̄, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heeg...

We realise Stroppel’s extended arc algebra \[13, 51] in the Fukaya–Seidel category of a natural Lefschetz fibration on generic fibre adjoint quotient map type $A$ nilpotent slice with two Jordan blocks, and hence obtain symplectic interpretation certain parabolic two-block versions Bernstein–Gel’fand–Gel’fand $\\mathcal{O}$. As an application, we give new geometric construction spectral sequenc...

diadema setosum (leske, 1778), is one of the common echinoids widely distributed in the indo-west pacific ocean, where it occurs from the red sea, persian gulf and the east coast of africa to japan, australia and malaysia. to investigate the developmental basis of morphological changes in embryos and larvae, we documented the ontogeny of d. setosum in a controlled laboratory condition at the in...

A restricted dth power of an ideal I is obtained by restricting the exponent vectors allowed to appear on “natural” generating set Id, for some integer d. In this paper, we study homological properties powers complete intersections. We construct a generalization L-complex construction Buchsbaum and Eisenbud. use resolution compute explicit basis Koszul homology which allows us deduce that quoti...

Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each f. g. projective R/I-module V has an Rprojective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 → P0 for all n ≥ 1, if d = 1. This computation yields a new proof of the classical Adams-Riemann-R...