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Homotopy similarity of maps. Strong similarity

S. S. Podkorytov

Abstract

Given pointed cellular spaces $X$ and $Y$, $X$ compact, and an integer $r\ge0$, we define a relation $\overset r\approx$ on $[X,Y]$ and argue for the conjecture that it always coincides with the $r$-similarity $\overset r\sim$.

Homotopy similarity of maps. Strong similarity

Abstract

Given pointed cellular spaces and , compact, and an integer , we define a relation on and argue for the conjecture that it always coincides with the -similarity .

Paper Structure

This paper contains 25 sections, 111 equations.

Table of Contents

  1. § 1. Introduction
  2. § 2. Definition of strong similarity
  3. § 3. Filtrations $\langle(Y^X)^{(U)}\rangle^{(s)}_X$ and $\langle(Y^X)^T\rangle^{(s)}_X$.
  4. § 4. Primitive transforms
  5. § 5. Compositions and smash products
  6. § 6. Homotopy invariance
  7. § 7. More combining products
  8. § 8. Strong similarity for an admissible couple
  9. § 9. Presheaves and extenders
  10. § 10. The abstract fissilizer $\Phi_E$ on $\langle\underline M(E)\rangle$
  11. § 11. Topological and simplicial constructions
  12. § 12. Canonical retractions in the cones ${\boldsymbol{\check{\mathsf C}}}{\gsfb b}\triangle E$ and ${\check{\mathrm C}}\Delta E$
  13. § 13. The fissilizer $\Phi_E$ on $\langle(Y^X_a)^{{\check{\mathrm C}}\Delta E}\rangle$
  14. § 14. Strong $1$-similarity
  15. § 15. Two identities
  16. ...and 10 more sections