相关论文: Some recent approaches in 4-dimensional surgery th…

Berge in [1] defined doubly primitive knots, which yield lens spaces by Dehn surgery. At the same paper he listed the knots into several types. In this paper we will prove the list is complete when $\tau>1$. The invariant $\tau$ is a…

We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of…

The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincar\'{e} duality complexes (PD complexes). The problem is that an arbitrary generalized manifold $X$ is always an ENR space, but it is…

There are many results showing the connection and phenomenon between some low-dimensional manifolds with the profinite completions of their fundamental groups. We focus on some Seifert 4-manifolds about the extent of their profinite…

We study cobordisms of a class of topological operads called ``manifold operads''. These operads are generalizations of the Fulton-MacPherson operad: an operad built from configurations of points in Euclidean space. Cobordism of manifold…

We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of…

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This…

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy…

The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes' programme where a geometrical structure…

In this paper we will show that two surfaces of the same genus and homology class in a simply connected 4-manifold are concordant. We will show they are often topologically isotopic when their complements have cyclic fundamental group.…

We study the four-dimensional effective theory arising from ten-dimensional heterotic supergravity compactified on manifolds with torsion. In particular, given the heterotic superpotential appropriately corrected at $\mathcal{O}(\alpha')$…

We study the topology and geometry of those compact Riemannian (4n)-manifolds (M,g), n > 1, with positive scalar curvature and holonomy in Sp(n)Sp(1). Up to homothety, we show that there are only finitely many such manifolds of any…

The classical Poincar{\'e} conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizations of 3-manifolds. A new confirmation of this conjecture…

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…

When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery…

Let M be a Poincare duality space of dimension at least four. In this paper we describe a complete obstruction to realizing the diagonal map M -> M x M by a Poincare embedding. The obstruction group depends only on the fundamental group and…

We prove that the stable moduli space of $(n-1)$-connected, $n$-parallelizable, $(2n+1)$-dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq 7$. The main novel ingredient is a version of the cobordism…

Thom-Pontrjagin constructions are used to give a computable necessary and sufficient condition when a homomorphism $\phi : H^n(L;Z)\to H^n(M;Z)$ can be realized by a map $f:M\to L$ of degree $k$ for closed $(n-1)$-connected $2n$-manifolds…

This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias…

After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then…