Submission ‟Ideal Triangulations and Once-Punctured Surface Bundles” for Low-Dimensional Topology

A well-known result of Walsh states that if $\mathcal{T}^ $i s a n i d e a l t r i a n g u l a t i o n o f a n a t o r o i d a l, a c y l i n d r i c a l, i r r e d u c i b l e, c o m p a c t 3 - m a n i f o l d w i t h t o r u s b o u n d a r y c o m p o n e n t s a n d$ \mathcal{T}^ $h a s e s s e n t i a l e d g e s, t h e n e v e r y p r o p e r l y e m b e d d e d, t w o - s i d e d, i n c o m p r e s s i b l e s u r f a c e$ S $i s i s o t o p i c t o a s p u n - n o r m a l s u r f a c e i n$ \mathcal{T}^* $u n l e s s$ S $i s i s o t o p i c t o a f i b e r o r v i r t u a l f i b e r . F o r a g i v e n m a n i f o l d$ M $t h a t f i b e r s o v e r$ S^1 $, i t w a s p r e v i o u s l y u n k n o w n w h e t h e r t h e r e e x i s t s a n i d e a l t r i a n g u l a t i o n i n w h i c h t h e f i b e r a p p e a r s a s a s p u n - n o r m a l s u r f a c e . W e p r o v e t h a t s u c h a t r i a n g u l a t i o n e x i s t s a n d g i v e a n a l g o r i t h m t o c o n s t r u c t t h e i d e a l t r i a n g u l a t i o n p r o v i d e d$ M$ has a single boundary component.

ScholarLattice

Ideal Triangulations and Once-Punctured Surface Bundles

Birch Bryant ⟨bbryant3@una.edu⟩