Open AccessOn the Geometric Algebra and Homotopy
Author(s) -
Yousuf Alkhezi
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n2p52
Subject(s) - mathematics , counterexample , homotopy , algebra over a field , tensor product , geometric algebra , pure mathematics , tensor (intrinsic definition) , n connected , discrete mathematics , filtered algebra
This paper aims at evaluating geometric algebra’s applications and characteristics, as well as assessing the new characteristic known as pinched homotopy. We elaborate a new approach to the pinched tensor and present the impact of such tensor on the homotopy. We also substitute the ordinary tensor product with the pinched one. Motivated by the different properties of the two tensors, we study several cases on which the difference is shown with providing counterexamples. The proof of some theorems ensure this approach.