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Tangential smoothings of $k$-fold connected sum of complex projective spaces

Priyanka Magar-Sawant

Abstract

This paper determines tangential structure set of $\#_k\mathbb{C}P^{n}$, for $3\leq n \leq 7$, by analyzing their stable cohomotopy groups and $KO$-groups. As a consequence, it establishes the existence of manifolds with tangential homotopy type but not homeomorphic to $\#_k\mathbb{C}P^{n}$ for $n=4,5$.

Tangential smoothings of $k$-fold connected sum of complex projective spaces

Abstract

This paper determines tangential structure set of , for , by analyzing their stable cohomotopy groups and -groups. As a consequence, it establishes the existence of manifolds with tangential homotopy type but not homeomorphic to for .
Paper Structure (7 sections, 20 theorems, 5 equations)

This paper contains 7 sections, 20 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Stable cohomotopy groups
  3. Reduced K-groups
  4. Complex K-groups
  5. Real K-groups
  6. Smooth normal invariant set
  7. Smooth tangential structure set

Key Result

Theorem A

Let $k,n\in\mathbb{N}$. Then

Theorems & Definitions (31)

  • Theorem A
  • Theorem B
  • Theorem C
  • Theorem 2.1: brumfiel1968
  • Theorem 2.2: RKSmoothStructuresonComplexProjectiveSpaces
  • Theorem 2.3: SB-RK-Priya2023smooth,Theorems 4.1 and 4.2
  • Theorem 2.4
  • Theorem 2.5
  • proof
  • Theorem 3.1
  • ...and 21 more