In this paper we prove that over local or global fields of characteristic 0, the Corestriction Principle holds for kernel and image of all maps which are connecting maps in group cohomology and the groups of R-equivalences. Some related questions over arbitrary fields of characteristic 0 are also discussed. AMS Mathematics Subject Classification (1991): Primary 11E72, Secondary 18G50, 20G10 Pla...

This manuscript is based on a ten hours series of seminars I delivered in August of 2003 at the Nagoya Institute of Technology as part of the workshop on homotopy theory organized by Norihiko Minami and following the Kinosaki conference in honor of Goro Nishida. One of the most striking applications of homotopy theory in “exotic” contexes is Voevodsky’s proof of the Milnor Conjecture. This conj...

A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself....

Suppose G is a finitely presented group that hyperbolic relative to P finite collection of proper subgroups G. Our main theorem states if the second cohomology H2(P,ZP) free abelian for each P?P, then H2(G,ZG) abelian. The problem reduces case when and members are 1-ended. In case, we prove “Cusped Space” this pair has semistable fundamental at ?. This provides starting point in our proof theor...

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetri...