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Divergence-free pseudopotentials for spatially even and odd-wave interactionsin spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bosemapping method is used to relate the effectively one-dimensional fermionicmany-body problem to that of a spinor Bose gas. Depending on the relativemagnitudes of the even and odd-wave interactions, the N-atom ground state mayhave total spin S=0, S=N/2, and possibly also intermediate values, the caseS=N/2 applying near a p-wave Feshbach resonance, where the N-fermion groundstate is space-antisymmetric and spin-symmetric. In this case the fermionicground state maps to the spinless bosonic Lieb-Liniger gas. An externalmagnetic field with a longitudinal gradient causes a Stern-Gerlach spatialseparation of the corresponding trapped Fermi gas with respect to variousvalues of $S_z$.Comment: 4+ pages, 1 figure, revtex4. Submitted to PRA. Minor corrections of  typos and notatio

Theory of spinor Fermi and Bose gases in tight atom waveguides