@article{oai:soar-ir.repo.nii.ac.jp:00012051, author = {ASADA, Akira}, issue = {2}, journal = {信州大学理学部紀要}, month = {Mar}, note = {In our previous paper ([1]), vector analysis on a Sobolev space Wk(X) was investigated and the possibility to give a geometric example of Kerner's higher gauge theory ([6],[7]) was discussed. In this paper, we give a simple example of geometric space on which the exterior derivation is not nilpotent but its n-th power vanishes (n≧3), by using suitable subspace of (∞-p)-forms. This provides a geometric example of Kerner's higher gauge theory. To discuss its algebraic counter part, we also treat Clifford algebra on Wk(X) with infinite degree spinors., Article, 信州大学理学部紀要 31(2): 59-70(1997)}, pages = {59--70}, title = {Vector Analysis on Sobolev Spaces, II}, volume = {31}, year = {1997} }