Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCellular chain complexes of universal covers of some 3-manifolds
131
0
0.0
(
0
)
Authors
Takefumi Nosaka
Ask ChatGPT about the research
No Arabic abstract
For a closed 3-manifold $M$ in a certain class, we give a presentation of the cellular chain complex of the universal cover of $M$. The class includes all surface bundles, some surgeries of knots in $S^3$, some cyclic branched cover of $S^3$, and some Seifert manifolds. In application, we establish a formula for calculating the linking form of a cyclic branched cover of $S^3$, and develop procedures of computing some Dijkgraaf-Witten invariants.
rate research
Read More
In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(mathbb{Z}_2)^3$-action such that its orbit space is a simple convex 3-polytope. We introduce six equivariant operations on 3-dimensional small covers. These six operations are interesting because of their combinatorial natures. Then we show that each 3-dimensional small cover can be obtained from $mathbb{R}P^3$ and $S^1timesmathbb{R}P^2$ with certain $(mathbb{Z}_2)^3$-actions under these six operations. As an application, we classify all 3-dimensional small covers up to $({Bbb Z}_2)^3$-equivariant unoriented cobordism.
Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete classification of compact 3-manifolds with empty or toroidal boundary which have the above property. We also discuss related group-theoretic questions.
In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $Theta$-graphs. As corollaries of this, we obtain some new results on codimension 1 embeddings and pseudo-isotopies of 4-manifolds. In the proof of the non-triviality of the diffeomorphisms, we utilize a twisted analogue of Kontsevichs characteristic class for smooth bundles, which is obtained by extending a higher dimensional analogue of March{e}--Lescops equivariant triple intersection in configuration spaces of 3-manifolds to allow Lie algebraic local coefficient system.
Let $N$ be a prime 3-manifold that is not a closed graph manifold. Building on a result of Hongbin Sun and using a result of Asaf Hadari we show that for every $kinBbb{N}$ there exists a finite cover $tilde{N}$ of $N$ such that $|operatorname{Tor} H_1(tilde{N};Bbb{Z})|>k$.
In this paper, it is explained that a topological invariant for 3-manifold $M$ with $b_1(M)=1$ can be constructed by applying Fukayas Morse homotopy theoretic approach for Chern--Simons perturbation theory to a local system on $M$ of rational functions associated to the free abelian covering of $M$. Our invariant takes values in Garoufalidis--Rozanskys space of Jacobi diagrams whose edges are colored by rational functions. It is expected that our invariant gives a lot of nontrivial finite type invariants of 3-manifolds.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
