I have difficulty understanding Sarkar's maslov index formula in symmetric products from http://arxiv.org/abs/math/0609673.

If $D$ is an $n$-sided region with corner points $p_1,\ldots, p_n$ then it reads like

$\mu(D)= \mu_{p_1}(D)+\mu_{P_n}(D)+ e(D)-g(n-2)/2+\sum_{ 1< i< j \leq n} \partial_j(D) \cdot \partial_i(D)$

where $\mu_{P_i}$ and $e$ are the point and euler measures.

First of all it seems to treat $P_1,P_n$ different from other points. Secondly he says the euler measure of an $n$ sided region is $1-n/4$ which looks different from what Lipshitz says (which takes the accute and obtuse corners into account). Last but not least I don't understand the definition of the last term. It is defined by moving the two sides in 4 different directions in such a way that no endpoint of one is on another and then taking intersection points. It's not clear for me what these 4 directions are and why the result is not always zero.