We correct a mistake on the citation of JSJ theory in [4]. Some arguments in [4] are also slightly modified accordingly. An important step in [4] uses JSJ theory [2, 3] to deduce some topological information about the knot complement when the knot Floer homology is monic, see [4, Section 6]. The version of JSJ theory cited there is from [1]. However, as pointed out by Kronheimer, the definition...

A finite graph Γ is G-symmetric if it admits G as a group of automorphisms acting transitively on V (Γ) and transitively on the set of ordered pairs of adjacent vertices of Γ. If V (Γ) admits a nontrivial G-invariant partition B such that for blocks B,C ∈ B adjacent in the quotient graph ΓB relative to B, exactly one vertex of B has no neighbour in C, then we say that Γ is an almost multicover ...

In this paper we give a positive answer to question of Dimca and Greuel about the quotient between Milnor Tjurina numbers for any irreducible germ plane curve singularity. This result is based on closed formula minimal number an equisingularity class in terms sequence multiplicities strict transform along resolution. The key points proof are previous results by Genzmer, Wall Mattei.

We study a finite-dimensional quotient of the Hecke algebra of type H n for general n, using a calculus of diagrams. This provides a basis of monomials in a certain set of generators. Using this, we prove a conjecture of C.K. Fan about the semisimplicity of the quotient algebra. We also discuss the cellular structure of the algebra, with certain restrictions on the ground ring. To appear in " M...

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G2 and Spin(7) holonomy. We derive mirror pairs of N = 1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a “G2 quotient construction” of non-compa...

In the two-person nim-type game called Euclid a position consists of a pair (a, b) of positive integers. Players alternate moves, a move consisting of decreasing the larger number in the current position by any positive multiple of the smaller number, as long as the result remains positive. The first player unable to make a move loses. In the restricted version a set of natural numbers Λ is giv...

In this paper, we characterize both closed and strongly subobjects in the category of bounded uniform filter spaces introduce two notions closure operators which satisfy weakly hereditary, idempotent productive properties. We further each Tj (j= 0,1) using these examine that them form quotient-reflective subcategories spaces. Also, connected Finally, ultraconnected objects topological relations...

We define the degenerate two boundary affine Hecke-Clifford algebra H d , and show it admits a well-defined q ( n ) -linear action on tensor space M ? N V where is natural module for are arbitrary modules Lie superalgebra of Type Q. When irreducible highest weight parameterized by staircase partition single row, respectively, this factors through quotient . then construct explicit quotient, p u...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V which satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respe...