Following this, he made contributions in operator K-theory and index theory, which culminated in the Baum–Connes conjecture.
fˈɑːloʊɪŋ ðˈɪs, hiː mˌeɪd kˌɑːntɹɪbjˈuːʃənz ɪn ˈɑːpɚɹˌeɪɾɚ kˈeɪθˈiəɹi ænd ˈɪndɛks θˈiəɹi, wˌɪtʃ kˈʌlmᵻnˌeɪɾᵻd ɪnðə bˈaʊm kˈɑːnz kəndʒˈɛktʃɚ.