The fundamental group of the torus is just the direct product of the fundamental group of the circle with itself:

  
    
      
        
          π
          
            1
          
        
        (
        
          
            T
          
          
            2
          
        
        )
        =
        
          π
          
            1
          
        
        (
        
          S
          
            1
          
        
        )
        ×
        
          π
          
            1
          
        
        (
        
          S
          
            1
          
        
        )
        ≅
        
          Z
        
        ×
        
          Z
        
        .
University of Hong Kong developed a liquid form of arsenic trioxide that can be given by mouth. Organoarsenic compounds, such as feed additives (roxarsone) and medication (neosalvarsan), are derived from arsenic trioxide. Manufacturing
Industrial uses include usage as a precursor to forestry products, in colorless glass production, and in electronics. Being the main compound of arsenic, the trioxide is the precursor to elemental arsenic, arsenic alloys, and arsenide semiconductors. Bulk arsenic-based compounds sodium arsenite and sodium cacodylate are derived from the trioxide.A variety of applications exploit arsenics toxicity, including the use of the oxide as a wood preservative. Copper arsenates, which are derived from arsenic trioxide, are used on a large scale as a wood preservative in the U.S. and Malaysia, but such materials are banned in many parts of the world. This practice remains controversial. In combination with copper(II) acetate, arsenic trioxide gives the vibrant pigment known as Paris green used in paints and as a rodenticide. This application has been discontinued. Alternative medicine
Despite the well known toxicity of arsenic, arsenic trioxide was used in traditional Chinese medicine, where it is known as pi-shuang (Chinese: 砒霜; pinyin: pīshuāng; lit. arsenic frost). In homeopathy, it is called arsenicum album. Some discredited patent medicines, e.g., Fowlers solution, contained derivatives of arsenic oxide. Toxicology
Arsenic trioxide is readily absorbed by the digestive system: toxic effects are also well-known upon inhalation or upon skin contact.