Eukaryotic genomes are folded into three-dimensional structures, such as self-associating topological domains, the borders of which are enriched in cohesin and CCCTC-binding factor (CTCF) required for long-range interactions1,2,3,4,5,6,7. How local chromatin interactions govern higher-order folding of chromatin fibres and the function of cohesin in this process remain poorly understood. Here we perform genome-wide chromatin conformation capture (Hi-C) analysis8 to explore the high-resolution organization of the Schizosaccharomyces pombe genome, which despite its small size exhibits fundamental features found in other eukaryotes9. Our analyses of wild-type and mutant strains reveal key elements of chromosome architecture and genome organization. On chromosome arms, small regions of chromatin locally interact to form ‘globules’. This feature requires a function of cohesin distinct from its role in sister chromatid cohesion. Cohesin is enriched at globule boundaries and its loss causes disruption of local globule structures and global chromosome territories. By contrast, heterochromatin, which loads cohesin at specific sites including pericentromeric and subtelomeric domains9,10,11, is dispensable for globule formation but nevertheless affects genome organization. We show that heterochromatin mediates chromatin fibre compaction at centromeres and promotes prominent inter-arm interactions within centromere-proximal regions, providing structural constraints crucial for proper genome organization. Loss of heterochromatin relaxes constraints on chromosomes, causing an increase in intra- and inter-chromosomal interactions. Together, our analyses uncover fundamental genome folding principles that drive higher-order chromosome organization crucial for coordinating nuclear functions.