Related papers: Combinatorial spin structures on triangulated mani…
This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion $\spinc$ structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are…
We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of…
This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost…
From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a…
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special K\"ahler holonomy. Motivated by certain curvature…
A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The…
We consider a family of cyclic presentations and show that, subject to certain conditions on the defining parameters, they are spines of closed 3-manifolds. These are new examples where the reduced Whitehead graphs are of the same type as…
The theme is the influence of the spin structure on the Dirac spectrum of a spin manifold. We survey examples and results related to this question.
Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups…
In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(\chi, c)$ lying in $0 \leq c \leq 8.76\chi$. Furthermore, as a corollary, we prove…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and $p$-gonal surfaces defined by divisors supported on their branch points. Moreover, we…
The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic…
We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth…
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…
The question of which manifolds are spin or spin^c has a simple and complete answer. In this paper we address the same question for spin^h manifolds, which are less studied but have appeared in geometry and physics in recent decades. We…
In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.