Algebraic topology for proper shape theory

Algebraic Topology Notes: Homotopy Theory

Notes on homotopy theory, the first part of a trilogy on algebraic topology. Any typos, errors, mistakes, gaffes, etc., are entirely my folly.

Categorically-algebraic topology and its applications

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

Topology Proceedings 1 (1976) pp. 115-124: ALGEBRAIC INVARIANTS IN SHAPE THEORY

Algebraic Topology

This manuscript will be published as Chapter 5 in Wiley’s textbook Mathematical Tools for Physicists, 2nd edition, edited by Michael Grinfeld from the University of Strathclyde. The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebr...

Algebraic Topology

Algebraic topology is at a point of inflection today, and the Spring 2014 Algebraic Topology program at MSRI reflects the excitement of this moment. The introductory workshop, with more than 200 participants, provided careful introductions to the dominant themes leading up to this moment, giving an informative welcome to the many young researchers in the program and attending the conference. Th...