We construct an explicit diffeomorphism between the Sasaki-Einstein spaces Y p,q and the product space S × S in the cases q 6 2. When q = 1 we express the Kähler quotient coordinates as an SU(2) bundle over S which we trivialize. When q = 2 the quotient coordinates yield a non-trivial SO(3) bundle over S with characteristic class p, which is rotated to a bundle with characteristic class 1 and r...

There are well-known characterizations of the hereditary quotient maps in the category of topological spaces, (that is, of quotient maps stable under pullback along embeddings), as well as of universal quotient maps (that is, of quotient maps stable under pullback). These are precisely the so-called pseudo-open maps, as shown by Arhangel’skii, and the bi-quotient maps of Michael, as shown by Da...

For self-orthogonal modules T , the quotient triangulated categories D(A)/K(addT ) are studied, in particular, their relations with the stable categories of some Frobenius categories are investigated. New descriptions of the singularity categories of Gorenstein algebras are obtained; and the derived categories of Gorenstein algebras are explicitly given, inside the stable categories of the grad...

We show that for any C∗-algebra A, a sufficiently large Hilbert space H and a unit vector ξ ∈ H, the natural application rep(A:H) θξ −−→ Q(A), π 7→ 〈π(−)ξ, ξ〉 is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C∗...

We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .

These are expanded notes from a set of lectures given at the school “Actions Hamiltoniennes: leurs invariants et classification” at Luminy in April 2009. The topics center around the theorem of Kempf and Ness [58], which describes the equivalence between the notion of quotient in geometric invariant theory introduced by Mumford in the 1960’s [80], and the notion of symplectic quotient introduce...

the subgroup of diffeomorphisms homotopic to the identity map. It acts naturally on the space ML(S) of compactly supported measured laminations on S: a piecewise linear space associated to S, whose quotient by the scalars PML(S) can be viewed as a boundary of the Teichmüller space T (S) (see Section 2 for more details on measured laminations and Teichmüller spaces). The space ML(S) has a piecew...

Let Knots be the abelian monoid of isotopy classes of knots S ⊂ S under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-OrrTeichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . . The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice kn...

It has been demonstrated that social exclusion, or ostracism, results in a decrease in four fundamental human needs: belonging, control, self-esteem, and meaningful existence. We replicated these results, and examined how empathizing and systemizing cognitive styles accounts for variation in the experience of social exclusion (self-reported distress and the four fundamental needs) during an int...