Have you not omitted "of Astrakhan"? Isn't the full quote (from Sherlock Holmes) "Heavy bands of Astrakhan were slashed across the sleeves and fronts of his double-breasted coat" ? In other words, there were strips of Astrakhan attached to the sleeves and front of his coat in a decorative fashion.

slash (verb)=To create slashes in a garment. slash (noun)=A slit in an outer garment exposing a lining or inner garment, usually of a contrasting color or design; any intentional long vertical cut in a garment. https://en.wiktionary.org/wiki/slash#Etymology_1 Here you can see an example of slashes. You can see the white inner garment sticking out through the slashed outer garment: https://s-media-cache-ak0.pinimg.com/originals/c1/4b/85/c14b852bcad061eb1400f6802724603d.jpg I'm not sure if you'll be able to see the above picture. Otherwise google "slashing fashion". Then you can see examples of this technique. Another picture: http://www.medievalhistories.com/strange-fashion/

Lyuba, the verb 'to slash' means 'to cut something, typically by using a knife or sword'. In other words, the man used a knife or sharp object to cut horizontal lines into the sleeves of his coat. I hope that helps :-) -Tom