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Concordance structure set of connected sum of projective spaces

Priyanka Magar-Sawant

Abstract

In this paper, the concordance structure set of connected sums of complex and quaternionic projective spaces in the real $n$-dimensional range with $8\leq n\leq 16$ is computed. It is demonstrated that the concordance inertia group of a connected sum equals the sum of individual concordance inertia groups. Furthermore, the concordance structure sets of manifolds and their connected sums are compared.

Concordance structure set of connected sum of projective spaces

Abstract

In this paper, the concordance structure set of connected sums of complex and quaternionic projective spaces in the real -dimensional range with is computed. It is demonstrated that the concordance inertia group of a connected sum equals the sum of individual concordance inertia groups. Furthermore, the concordance structure sets of manifolds and their connected sums are compared.
Paper Structure (4 sections, 15 theorems, 17 equations)

This paper contains 4 sections, 15 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Maps from the connected sum of manifolds to homotopy commutative H-groups
  3. Sum formula and the concordance structure set of projective spaces
  4. Concordance structure set of k-fold connected sum of projective spaces

Key Result

Theorem 1.1

The concordance structure sets $\mathcal{C}{\left({\#}_k\mathbb{C}\mathrm{P}^{n}\right)}$ for $4\leq n\leq 8$, $\mathcal{C}{\left({\#}_k\mathbb{C}\mathrm{P}^{2n}{\#}_l\mathbb{H}\mathrm{P}^{n}\right)}$ for $2\leq n\leq 4$, and $\mathcal{C}{\left({\#}_k\mathbb{C}\mathrm{P}^{8}{\#}_l\mathbb{H}\mathrm{P

Theorems & Definitions (26)

  • Definition 1.1
  • Theorem 1.1
  • Definition 1.2
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • ...and 16 more