Related papers: Stiefel-Whitney Numbers for Singular Varieties

Let $G$ be a finite group and $P$ a Sylow $2$-subgroup of $G$. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of $G$ in terms of the size of the abelianization of $P$. To do…

We give a bound on the number of weighted real forms of a complex variety with finite automorphism group, where the weight is the inverse of the number of automorphisms of the real form. We give another bound involving the Sylow 2-subgroup…

In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G.…

We construct Euler and Stiefel-Whitney classes of vector bundles with quadratic form by analyzing the intersection theory of the associated quadric bundles. We also compute the Chow rings of quadric and isotropic flag bundles. Along the…

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

In this paper, we view the equivariant orientation theory of equivariant vector bundles from the lenses of equivariant Picard spectra. This viewpoint allows us to identify, for a finite group $\mathrm{G}$, a precise condition under which an…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

In this paper, we introduce the notion of spectral genus $\widetilde{p}_{g}$ of a germ of an isolated hypersurface singularity $(\mathbb{C}^{n+1}, 0) \to (\mathbb{C}, 0)$, defined as a sum of small exponents of monodromy eigenvalues. The…

We show that for smooth complex projective varieties the most general combinations of chern numbers that are invariant under the K-equivalence relation consist of the complex elliptic genera. Combined with a recent result of Totaro, we…

In this paper we prove new explicit formulas for Faltings' $\delta$-invariant of an arbitrary hyperelliptic Riemann surface. This has several applications: For example we obtain an explicit lower bound for $\delta$ depending only on the…

We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-S\"oderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of…

We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…

We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are…

We completely determine the mod $2$ Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth $4$-manifold $X$. Our computation confirms the validity of the simple type conjecture mod $2$ for spin structures. Our…

On a compact oriented four-manifold with an orientation preserving involution c, we count solutions of Seiberg-Witten equations, which are moreover symmetrical in relation to c, to construct "real" Seiberg-Witten invariants. Using Taubes'…

We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of the Witten genus, which exhibits a close relationship to recent work on non-equivariant…

In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for…

It is known that, for all n, there exist compact differentiable orientable n-manifolds with dual Stiefel-Whitney class wbar_{n-ahat(n)} nonzero, and this is best possible, but the proof is nonconstructive. Here ahat(n) equals the number of…

We introduce a theoretical framework that connects multi-chart autoencoders in manifold learning with the classical theory of vector bundles and characteristic classes. Rather than viewing autoencoders as producing a single global Euclidean…

We classify the reflexive modules of rank one over rational and minimally elliptic singularities. Equivalently, we classify full line bundles on the resolutions of rational and minimally elliptic singularities. As an application, we…