Related papers: PL cobordism and classification of PL manifolds
In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from…
We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…
In this note I give a positive solution to Bullett's conjecture (posed in [1]) regarding a geometric presentation of the universal mod $p$ oriented ring spectrum.
We compute the equivariant (stable) complex cobordism ring $(MU_G)_*$ for finite abelian groups $G$.
We compute the cohomology of crystallographic groups with holonomy of prime order. As an application we compute the group of gerbes associated to many six--dimensional toroidal orbifolds arising in string theory.
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
(Co)bordisms of manifolds and maps are fundamental and important objects in algebraic and differential topology of manifolds and related studies were started by Thom etc.. Cobordisms of Morse functions were introduced and have been studied…
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.
We show that two 3-manifolds that admit Sol geometry and have first homology group of order 16 are integer homology cobordant if and only if they are homeomorphic.
In this paper we classify the closed orientable manifolds of arbitrary dimension.
The notion of 2-framed three-manifolds is defined. The category of 2-framed cobordisms is described, and used to define a 2-framed three-dimensional TQFT. Using skeletonization and special features of this category, a small set of data and…
Recently Galatius, Madsen, Tillmann and Weiss identified the homotopy type of the classifying space of the cobordism category of embedded d-dimensional manifolds [7] for each positive integer d. Their result lead to a new proof of the…
We use 4-valent planar graphs and singular cobordisms (called foams) to construct an integral doubly-graded cohomology for tangles, and in particular for links, whose graded Euler characteristic yields the sl(n) link polynomial (for n > 3).
This paper discusses the cobordism of Lagrangian submanifolds (in the monotone setting) and structures it as a category that is related in a functorial way to an appropriate (derived) Fukaya category. Are also discussed obstructions to…
It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod 2 homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it…
The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
In this paper we introduce the notion of exact links, which constitute a broad class of high dimensional links.
We obtain a solution to a bordism version of Gromov's linearity problem over a large family of acyclic groups, for manifolds with arbitrary dimension. Every group embeds into some acyclic group in this family. Thus, the linear bordism…
We introduce a new stable range invariant for the classification of closed, oriented topological $4$-manifolds (up to $s$-cobordism), after stabilization by connected sum with a uniformly bounded number of copies of $S^2\times S^2$.