Related papers: Cobordism invariants from BPS q-series

In this article, we answer two questions of Buchanan-McKean (arXiv:2312.08209) about bordism for manifolds with spin$^h$ structures: we establish a Smith isomorphism between the reduced spin$^h$ bordism of $\mathbb{RP}^\infty$ and…

We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with…

Generating functions of BPS invariants for N=4 U(r) gauge theory on a Hirzebruch surface with r=2 and 3 are computed. The BPS invariants provide the Betti numbers of moduli spaces of semi-stable sheaves. The generating functions for r=2 are…

In this paper, we investigate birational toric morphisms between quantum toric stacks -- namely, toric (analytic) stacks associated with fans whose cones may be irrational -- focusing on two primary classes of examples: weighted blow-ups…

The cobordism invariance of the index on closed manifolds is reproved using the calculus of cusp pseudodifferential operators on a manifold with boundary. More generally, on a compact manifold with corners, the existence of a symmetric cusp…

Although it is well-known that the complex cobordism ring is a polynomial ring $\Omega_{*}^{U}\cong\mathbb{Z}\left[\alpha_{1},\alpha_{2},\ldots\right]$, an explicit description for convenient generators $\alpha_{1},\alpha_{2},\ldots$ has…

A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

We demonstrate that it is conceptually and computationally favorable to regard spin-weighted spherical harmonics as vector valued functions on the total space $SO(3)$ of the Hopf bundle, satisfying a covariance condition with respect to the…

This paper explores the possibility of constructing multivariate generating functions for all cohomology dimensions of all holomorphic line bundles on certain complex projective varieties of Fano, Calabi-Yau and general type in various…

Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…

K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface string theory associates an…

We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…

Within the theoretical framework we apply, a suggested origin for single spin asymmetries is the presence of gauge links in transverse momentum dependent distribution functions. Recently we found new gauge link structures in a number of…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

Ambi-polar metrics, defined so as to allow the signature to change from +4 to -4 across hypersurfaces, are a mainstay in the construction of BPS microstate geometries. This paper elucidates the cohomology of these spaces so as to simplify…

Cobordism groups and cut-and-paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union. By imposing both relations simultaneously, a cobordism cut and paste group…

Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…

We define $p$-adic BPS or $p$BPS-invariants for moduli spaces $M_{\beta,\chi}$ of 1-dimensional sheaves on del Pezzo surfaces by means of integration over a non-archimedean local field $F$ . Our definition relies on a canonical measure…

We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible…

We investigate topology change in 3D. Using Morse theory and handle decomposition we find the set of elementary cobordisms for 3-manifolds. These are: (i) \O <-> S^2; (ii) \Sigma_g <-> \Sigma_{g+1}; (iii) \Sigma_{g_1} \sqcup \Sigma_{g_2}…