Topological Analysis of Point Singularities in Stimulus Preference Maps of the Primary Visual Cortex

A lar ge p op u lat ion of n eu r on es in t h e p r im ar y v isu al cor t ex op t im ally r esp on d t o t h e or ien t at ion an d p h ase of a gr at in g st im u lu s in lu m in an ce. I d em on st r at e h er e t h at t h e t op ology of t h e st im u lu s sp ace sp an n ed b y t h ese p ar am et er s is eq u iv alen t t o t h at of t h e Klein bottle, which has a characteristic feature in that there is no distinction b et w een t h e in sid e an d ou t sid e of t h e b ot t le. Th e assu m p t ion t h at t h ese st im u lu s p ar am et er s ar e con t in u ou sly ar r an ged alm ost ev er y w h er e on t h e v isu al cor t ical su r face en ab les u s t o m ap fr om a loop on the cortical surface to a loop on the Klein bottle. This leads to a sy st em at ic cat egor isat ion of p ossib le p oin t sin gu lar it ies in t h e arrangements of the optimal orientation and phase in the cortex. Two t y p es of p oin t sin gu lar it ies h av e b een ob ser v ed in t h e or ien t at ion p r efer en ce m ap , accor d in g t o clock w ise or cou n t er clock w ise r ot at ion in op t im al or ien t at ion ar ou n d t h e p oin t s. Th e p r esen t an aly sis p r ed ict s t h at each t y p e of or ien t at ion cen t …