A paper of 120 pages by KIHARA Hiroshi Senior Associate Professor at the University of Aizu, has been decided to be published in Memoirs of the American Mathematical Society (※1), a publication of the American Mathematical Society (※2).
Details of the journal
Name of Journal: Memoirs of the American Mathematical Society
Scheduled date of publication: undecided (already accepted)
Details of the paper
Title of paper：Smooth Homotopy of Infinite-Dimensional C^∞-Manifolds
Author: KIHARA Hiroshi (Mathematics and Physics Laboratory Group)
Link to publication
※ In this paper, I use the notion of a diffeological space along with Quillen's (Daniel Quillen, American Fields Medallist) model categorical framework to develop a homotopy theory which enables us to deal with smooth maps, and then apply it to infinite-dimensional C^∞-manifolds.
(The ordinary homotopy theory deals with topological spaces and continuous maps. Thus, the principal part of this paper is devoted to the construction of a homotopy theory for the study of infinite-dimensional C^∞-manifolds and smooth maps.)