Ordered Group Invariants for One-dimensional Spaces
نویسنده
چکیده
We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.
منابع مشابه
The Universal Order One Invariant of Framed Knots in the Total Spaces of S-bundles over Orientable Surfaces
It is well-known that self-linking is the only Z-valued Vassiliev invariant of framed knots in S. However for most 3-manifolds, in particular for the total spaces of S-bundles over an orientable surface F 6= S, the space of Z-valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S-bundles over...
متن کاملEquivariant Cohomology and Wall Crossing Formulas in Seiberg-Witten Theory
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu [7] and Okonek-Teleman [8] for Seiberg-Witten invariants. One of the difficulties in the study of Donaldson invariants or Seiberg-Witten invariants for closed oriented 4-manifold with b2 = 1 is that one has to deal with reducible solutions. There have been a lot of work in this ...
متن کاملNotes on some Distance-Based Invariants for 2-Dimensional Square and Comb Lattices
We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...
متن کاملA classification of finite rank dimension groups by their representations in ordered real vector spaces
This paper systematically studies finite rank dimension groups, as well as finite dimensional ordered real vector spaces with Riesz interpolation. We provide an explicit description and classification of finite rank dimension groups, in the following sense. We show that for each n, there are (up to isomorphism) finitely many ordered real vector spaces of dimension n that have Riesz interpolatio...
متن کاملGeneralized $F$-contractions in Partially Ordered Metric Spaces
We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...
متن کامل