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$K$-theory of co-existentially closed continua

Christopher J. Eagle, Joshua Lau

Abstract

We describe the possible values of $K$-theory for $C(X)$ when $X$ is a co-existentially closed continuum. As a consequence we also show that all pseudo-solenoids, except perhaps the universal one, are not co-existentially closed.

$K$-theory of co-existentially closed continua

Abstract

We describe the possible values of -theory for when is a co-existentially closed continuum. As a consequence we also show that all pseudo-solenoids, except perhaps the universal one, are not co-existentially closed.
Paper Structure (5 sections, 24 theorems, 22 equations)

This paper contains 5 sections, 24 theorems, 22 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. $K_0$ for co-existentially closed continua
  4. $K_1$ for co-existentially closed continua
  5. Continua that are not co-existentially closed

Key Result

Theorem 1.1

Let $X$ be a co-existentially closed continuum. Then $K_0(C(X)) = \mathbb{Z}$ and $K_1(C(X))$ is a torsion-free divisible abelian group that may have arbitrarily large rank.

Theorems & Definitions (53)

  • Theorem 1.1
  • Definition 2.2
  • Lemma 2.5
  • proof
  • Proposition 3.4
  • proof
  • Proposition 3.5
  • proof
  • Theorem 3.6
  • proof
  • ...and 43 more