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George Domat and
Paul Plummer
First cohomology of pure mapping class groups of big genus one and zero surfaces
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| Published: |
March 5, 2020. |
| Keywords: |
infinite-type surface; big mapping class groups; group cohomology; polish groups; automatic continuity. |
| Subject: |
57M07, 57S05, 20F65. |
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Abstract
We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to Z factors through a sphere with finitely many punctures. In fact, we get an uncountable family of such maps. |
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| Acknowledgements
Domat was partially supported by NSF DMS-1607236 amd NSF DMS-1840190.
Plummer was partially supported by NSF DMS-1651963 and NSF DMS-1611758.
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| Author information
George Domat:
Department of Mathematics
University of Utah
Salt Lake City, UT 84102, USA
domat@math.utah.edu
Paul Plummer:
Department of Mathematics
University of Oklahoma
Norman, OK 73019, USA
pplummer@math.ou.edu
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