Borsuk-Ulam Theorems and Their Parametrized Versions for F P-m x S-3

作者：Singh Somorjit Konthoujam; Singh Hemant Kumar^*; Singh Tej Bahadur

来源：Bulletin of the Brazilian Mathematical Society, 2018, 49(1): 179-197.

DOI：10.1007/s00574-017-0040-1

• Free action
• Finitistic space
• Leray-Serre spectral sequence
• Parametrized Borsuk-Ulam theorem
• Characteristic polynomial
• Partial coincidence set

Let a prime, act freely on a finitistic space X with mod p cohomology ring isomorphic to that of , where mod p and or . We wish to discuss the nonexistence of G-equivariant maps and , where is equipped with a free G-action. These results are analogues of the celebrated Borsuk-Ulam theorem. To establish these results first we find the cohomology algebra of orbit spaces of free G-actions on X. For a continuous map , a lower bound of the cohomological dimension of the partial coincidence set of f is determined. Furthermore, we approximate the size of the zero set of a fibre preserving G-equivariant map between a fibre bundle with fibre X and a vector bundle. An estimate of the size of the G-coincidence set of a fibre preserving map is also obtained. These results are parametrized versions of the Borsuk-Ulam theorem.

• 出版日期2018-3