Related papers: Exotic Differentiable Structures and General Relat…
In previous work, we proposed a general framework of positive topological field theories (TFTs) based on Eilenberg's notion of summation completeness for semirings. In the present paper, we apply this framework in constructing explicitly a…
This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…
We construct Anosov diffeomorphisms on manifolds that are homeomorphic to infranilmanifolds yet have exotic smooth structures. These manifolds are obtained from standard infranilmanifolds by connected summing with certain exotic spheres.…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
This thesis discusses exotic 7-spheres, i.e. manifolds that are homeomorphic but not diffeomorphic to the ordinary 7-sphere, using a set of analytical and computational tools from theoretical physics. The theory of fibre bundles and…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
Wall-type stabilization problems investigate the collapse of exotic 4-dimensional phenomena under stabilization operations (e.g., taking connected sums with $S^2 \times S^2$). We propose an elementary approach to these problems, providing a…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
We construct an infinite family of mutually non-diffeomorphic irreducible smooth structures on the topological 4-manifold $S^2 \times S^2$.
We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist.…
An anisotropic elastic material is referred to as exotic when, under specific loadings, its mechanical response exhibits a higher degree of symmetry than that prescribed by its intrinsic material symmetry. Such materials, which may be…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…
7-dimensional closed and simply-connected manifolds have been attractive as central and explicit objects in algebraic topology and differential topology of higher dimensional closed and simply-connected manifolds, which were studied…
We initiate the study of exotic Dehn twists along 3-manifolds $\neq S^3$ inside $4$-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more generally of definite 4-manifolds, and exotic…
We reprove and strengthen some old difficult theorems of 4-manifolds by the aid of recently discovered modern tools, which involve contact structures on 3-manifolds, compact Stein domains, etc.
We study the possibility of realizing exotic smooth structures on punctured simply connected $4$-manifolds as leaves of a codimension one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Beyond black holes and neutron stars, new hypothetical compact objects have been proposed as potential astrophysical entities. In general, their properties have not yet been fully explored or understood, nor has it been proven whether or…