Since we are considering the local degrees as when restricted to hemispheres Delta is a Homoemorphism that differ just by the composition of the Antipodal map WLOG we assume one of the local degree to be +1 other will be that of Antipodal, Hence finally what we get the total degree to be deg\Delta = 1+(-1)^k
In 1:10:49 why deg\Delta = 1+(-1)^k ? Where is the 1 come from?
Since we are considering the local degrees as when restricted to hemispheres Delta is a Homoemorphism that differ just by the composition of the Antipodal map WLOG we assume one of the local degree to be +1 other will be that of Antipodal, Hence finally what we get the total degree to be deg\Delta = 1+(-1)^k