The central disaster prevention council have pointed out the possibility of an earthquake directly below Tokyo metropolitan that would cause enormous damage to around Tokyo Bay. The damage estimates show that about 610,000 houses were completely destroyed and burned, with a maximum of 23,000 dead and a maximum of 72,000 casualties. Although measures against the earthquake have been elaborated in dealing with survivors, dealing with those who have died has not yet been sufficiently studied. For the deceased, it is necessary to have a solemn condolence without distinguishing between them, and it is necessary for disaster management to consider countermeasures.

In this study, from the viewpoint of civil engineering, based on wide-area crematories currently under study, we pointed out problems with the treatment capacity and spatial locations of crematoriums in consideration of the earthquake directly below the capital and proposed measures to improve disaster management.

This note is an appendix of Goto’s Master Dissertation³⁾. The subject is THEOREM 3.14 of Birman’s book¹⁾ which states that the kernel of the Gassner representation is a subset of the commutator subgroup of the pure braid group. When we prepared Goto’s Master Dissertation, we could not fill the space between the lines in the proof. THEOREM 3.14 deals with not only the kernel of Gassner representation but also the kernel of Burau representation which is a homomorphism from the braid group. The proof for Burau representation is done by considering the determinants of the image of the representation. The determinants are Laurant polynomials of one variable. It is stated in the proof that the case of Gassner representation is proved similarly. Since the determinants of this case are Laurant polynomials of multi variables, we need more consideration. After Goto’s Master Dissertation, we complete the proof for Gassner representation by elementary matrix calculation as we show here.