We replace our earlier condition that physical states of the superstring have non-negative grading by the requirement that they are analytic in a new real commuting constant t which we associate with the central charge of the underlying Kac-Moody superalgebra. The analogy with the twisted N=2 SYM theory suggests that our covariant superstring is a twisted version of another formulation with an ...

This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me remarkable) work of N. Ganter, relating replicability of McKay-Thompson series to the theory of exponential cohomology operations.

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of C2. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum Calogero-Sutherland many-body system. A relationship between the quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas correspondence for local curves is pr...

A field theoretical realization of topological gravity is discussed in the semirigid geometry context. In particular, its topological nature is given by the relation between deRham cohomology and equivariant BRST cohomology and the fact that all but one of the physical operators are BRST-exact. The puncture equation and the dilaton equation of pure topological gravity are reproduced, following ...

We analyze the circle-equivariant spectrum MStringC which is the equivariant analogue of the cobordism spectrum MU〈6〉 of stably almost complex manifolds with c1 = c2 = 0. In [Gre05], the second author showed how to construct the ring T-spectrum EC representing the T-equivariant elliptic cohomology associated to a rational elliptic curve C. In the case that C is a complex elliptic curve, we cons...

In recent years much attention has been given to a certain spectral sequence relating motivic cohomology to algebraic K-theory [Be, BL, FS, V3]. This spectral sequence takes on the form H(X,Z(− q 2 )) ⇒ K(X), where the H(X ;Z(t)) are the bi-graded motivic cohomology groups, and K(X) denotes the algebraic K-theory of X . It is useful in our context to use topologists’ notation and write K(X) for...

Abstract. Given an n-tuple of positive real numbers (α1, . . . , αn), Konno [K2] defines the hyperpolygon space X(α), a hyperkähler analogue of the Kähler variety M(α) parametrizing polygons in R3 with edge lengths (α1, . . . , αn). The polygon space M(α) can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector; from this point of view, X(...

We present a proof that the equivariant intersection cohomology of any complete algebraic variety acted by a connected algebraic group G is a free module over H∗(BG).

We approach Mackenzie’s LA-groupoids from a supergeometric point of view by introducing Q-groupoids. A Q-groupoid is a groupoid object in the category of Q-manifolds, and there is a faithful functor from the category of LA-groupoids to the category of Q-groupoids. Using this approach, we associate to every LA-groupoid a double complex whose cohomology simultaneously generalizes Lie groupoid coh...