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Full-Text Articles in Physical Sciences and Mathematics
Elementary Orbifold Differential Topology, Joseph E. Borzellino, Victor Brunsden
Elementary Orbifold Differential Topology, Joseph E. Borzellino, Victor Brunsden
Mathematics
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sardʼs theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold …
When Is A Trigonometric Polynomial Not A Trigonometric Polynomial?, Joseph E. Borzellino, Morgan Sherman
When Is A Trigonometric Polynomial Not A Trigonometric Polynomial?, Joseph E. Borzellino, Morgan Sherman
Mathematics
No abstract provided.
Temporal Topos And U-Singularities, Goro C. Kato
Temporal Topos And U-Singularities, Goro C. Kato
Mathematics
Several papers and books by C. Isham, C.Isham-A. Doering, F. Van Oystaeyen, A.Mallios-I. Raptis, C. Mulvey, and Guts and Grinkevich, have been published on the methods of categories and sheaves to study quantum gravity. Needless to say, there are well-written treatises on quantum gravity whose methods are non-categorical and non-sheaf theoretic. This paper may be one of the first papers explaining the methods of sheaves with minimally required background that retains experimental applications. Temporal topos (t-topos) is related to the topos approach to quantum gravity being developed by Prof. Chris Isham of the Oxford-Imperial research group (with its foundations inthe …