If on a hot Shabbat afternoon a man wishes to wear his sports jacket over his shoulders, rather than with his arms through the sleeves, may he wear the jacket in this fashion through a public domain (without an Eruv)? Do we consider the jacket as being worn, or does this constitute carrying, which is forbidden in a public domain on Shabbat?
The Gemara in Masechet Shabbat (58) addresses the case of a servant who misplaces the emblem his master had given him for identification, and fears that the master might interpret the emblem's absence as an attempt to rebel. The servant therefore wears his cloak in an unusual manner, over his shoulders, to conceal the area on his body where the emblem is normally worn. The Gemara establishes that if the servant walks through the public domain while wearing his cloak in this fashion he transgresses the Shabbat prohibition of carrying. Since he wears the cloak in a manner in which it is not normally worn, he is considered carrying, rather than wearing, the garment, and he thus violates Shabbat.
Would this ruling apply nowadays to a sports jacket worn over one's shoulders?
In the sefer, Shemirat Shabbat Ke'hilchata, in Perek 18, Halacha 4, it says that strictly speaking, one may wear a sports jacket over his shoulders in a public domain on Shabbat. Since many people customarily wear sports jackets in this fashion, it may be considered "Derech Malbush" – the conventional manner of wearing. Nevertheless, in the footnote, in s”k 24, better to be stringent because it may fall off and you might come to carry it.
Hacham Ben Sion Abba Shaul, however, in his work Or L'sion (vol. 2, perek 23, Halacha 7), ruled unequivocally that one may wear his sport jacket over his shoulders on Shabbat, given that this has become a normal manner of wearing a sports jacket. He adds (ibid, Halacha 8) that if a person goes to a Mikveh on Shabbat and wishes to bring a towel, he may "wear" the towel through a public domain by draping it over the shoulders the way we normally wear a Talit. Wearing a towel in this fashion is considered "Derech Malbush" and it may therefore be worn in this manner in a public domain on Shabbat.
Summary: One may wear a sports jacket over his shoulders in a public domain on Shabbat; similarly, one may wear a towel over his back like a Talit in a public domain on Shabbat.