arXiv subjects

Steve Gersten

Publications and source records attributed to Steve Gersten.

2 recordsLinked to original sources

arXiv2015

Topology of the Standard Model, I: Fermions

The Harari-Shupe model for fermions is extended to a topological model which contains an explanation for the observed fact that there are only three generations of fermions. Topological explanations are given for $β$-decay and for proton decay predicted in supersymmetry and string theories. An explanation is given for the observed fact that the three generations of fermions have such similar properties. The concept of "color" is incorporated into the model in a topologically meaningful way. Conservation laws are defined and discussed in the context of the algebraic topology of the model, and preon number is proved to be linearly determined by charge, weak isospin, and color.

physics.gen-ph↗

arXiv2015

Asphericity for certain groups of cohomological dimension 2

A finite connected 2-complex K whose fundamental group is of cohomological dimension 2 is aspherical iff the subgroup Σ_K of H_2(K) consisting of spherical 2-cycles is zero. A finite connected subcomplex of an aspherical 2-complex is aspherical iff its fundamental group is of cohomological dimension 2. If G is a countable group such that extension of scalars from Z[G] to \ell_2(G) kills \bar K_0(Z[G]), and if P is a finitely generated projective Z[G]-module with P/IP=0, where I is the augmentation ideal of Z[G], then P=0. In particular, if G is a countable group of cohomological dimension 2 and P is a finitely generated projective Z[G]-module such that P/IP=0, then P=0.

math.GR↗